Please could I try to help with some background information and a little of my own interpretation?
In my very humble opinion, I think that the situation of Beatrice and Eugenie owes itself to a number of interwoven facts that have suddenly all come to a head at the same time: Before trying to explore these in some more detail however, please could I start by dealing with the statement that I often see repeated in various places that Andrew is the Queen's favourite son? What I actually think is this: the Queen loves her children equally I am sure, but she seems to have a 'closeness' to Andrew and indeed Edward [The Queen reported spends a lot of time with Edward and Sophie at their home] which I think has arisen because of the circumstances surrounding their births: if we cast our minds back, Charles and Anne were born in 1948 and 1950 before the Queen suddenly found hereslf inheriting a position that she had assumed would not happen for some years, because of the relatively sudden and unexpected death of her father. Suddenly, in 1952 the Queen found herself both as the mother of two very small children and also as head of a Realm and a Commonwealth. Her succession responsibilities I am sure impacted on her family life as she struggled to find a balance; remember that back in the 1950's, monarchy was a very much formal affair that it seems today; also of course, even the 'business of royalty' took longer; air transport was slower, with longer plane journeys and no helicopters - in other words, being the 'Queen' took up a lot of the Queen's time, and in my very humble opinion took up a lot of her 'family' time, with the result that she saw less of her two elder children than she would probably have wanted.
By the time that Andrew and then Edward were born, I think that the Queen had both 'settled into her royal role' a lot better and of course was the beneficiary of the huge social changes of the 1960's that had begun to usher in a more informal style. The Queen reportedly had a lot more time to spend with Andrew and Edward [one of her biographers reported how he once found Andrew and Edward playing away on the floor whilst the Queen worked on her state business two feet away at her desk]. Thus, in my very humble opinion, the Queen developed a more 'informal closeness' to her two youngest, but she did not love them any more, or her two elder children any the less.
Now today's position; first, contemporary society allows a lot of outspoken criticism of the monarchy and the Royal Family which even 30 years ago did not exist so strongly. Today we are also facing a time of austerity - lots of families are in financial difficulties and the UK jobs situation at time seems pretty grim: the result of this is that 'too much flaunting of one's wealth' and 'too much public enjoyement' seems to be frowned on. Also of course, the events of 29 April 2011 have now 'secured' the outlook for the 'next generation' - in other words, it seems a convenient time for the Royals to 'take stock' of the current situation:
First, the Prince of Wales for some years has been talking about 'slimming down the monarchy' but even this has not been his sole preserve - look at the changes that the Queen herself has instigated - her decision to pay income tax, her decision to make Edward a Royal Earl rather than a Royal Duke, her decision to refund to the Treasury many of the annual Civil List payments made to her family [the Kents, Gloucesters] the decision to make Prince Michael of Kent pay an economic rent for his KP appartment etc etc.
The tone for a contraction of monarchy thus having been set, we now find ourselves at an ideal 'position' to move the implementation of these changes 'up a gear'. Prince William is now, to all intents and purposes, working as an 'ordinary' member of the armed forces rather than as a full time 'royal'; there is some public 'disquiet' at the cost of monarchy, and particularly the security costs of the DoY's daughters, particularly when Zara, herself a grandchild of the Queen, is without security protection. Princess Beatrice and Eugenie - Regardless of whether it is accurate or fair or kind - are seen to be costing the country £250,000 a year in security protection alone - they are also seen as 'unpopular', again regardless of whether it is accurate or fair or kind, as a result one suspects of the general dismay surrounding the DofY's Special Trade Representative role AND the continuing unpopularity of Sarah, Duchess of York, [whether fair or not is by-the-by: the problem is that 'perception is reality'] right down to the fact that most of the press coverage of Beatrice and Eugenie is concentrated on their alleged 'holiday, clubbing and partying lifestyle'.
With all of the foregoing, now seems to be good time for the Royal Family's image makers [basically BP courtiers, who one presumes must be acting on the advice of the Queen, because I am quite sure that NOTHING happens without HM's say-so] to announce the axing of the Princesses' security protection and the intention for B and E to have their own careers rather than a royal role.
For the future, I think that if Beatrice and Eugenie start careers, they should prefereably consider roles that do not in any way 'depend' on their 'royalty'. Don't forget how the Countess of Wessex tried to keep on her fomer PR job, but in fact was unable to do so and indeed became badly unstuck [as was revealed by the 'Fake Sheik' ] because her 'professional life' was 'boosted' by her newly-found royal status: there would not have been such a problem if (say) Sophie had been a teacher or a secretary. Don't forget that the most 'successful' working royals have been those who worked at roles which at least theoretically owed NOTHING to their royal status: the Duke of Kent and Prince Michael both had satisfactory service careers, the Duke of Gloucester [before he succeeded to his father's title] had been an architect; come to that, the DofY, Prince William and Prince Harry have all been applauded for their 'service' careers, rather than just their 'royal' careers. An honourable mention should also no doubt go to the present Duchess of Kent, who in recent times had been working as music teacher, based on her 'musical talent' rather than her 'royal position'.
If Beatrice and Eugenie do move to 'un-royal' careers or perhaps take up some form of profession, the next step might be to help their exit from 'front line' royal prominence by following royal precedent and give consideration to the removal of their royal titles and precedence, as was the case in 1919 when Princess Patricia renounced her princely title on her marriage to the Hon Alexander Ramsay in order to step back from a 'public' royal life. Unfair perhaps, but in this day and age, in my very humble opionion, the Monarchy is going to have to develop in order to preserve itself.
As a footnote, I think that much would be done to improve the Yorks' public image [however unfair it may sound] if Beatrice and Eugenie cut down on their foreign holidays and clubbing and if Sarah Duchess of York stepped permanantly OUT of the limelight. At the moment, the PERCEPTION is that most of the York family are 'running with the international white-trash jet set' [as it is known] and I don't think that this is helping with their image. Yes, it sounds unfair, and I accept that many people might think that this would have a negative impact on Sarah's charitable work, but the bottom line is that AT THE MOMENT and however UNFAIR it seems, in my humble opinion, the Yorks' popularity would best be servied by a period of withdrawal from public life. Please may I stress that I don't want this to be seen as 'Sarah bashing'; it is just that every time the Yorks put their heads 'above the parapet', HUGE negative publicity results however much it may not be the fault of the individuals, particularly Beatrice and Eugenie.
Just my thoughts,
Alex