It seems to me that Henrik was in a bit of a damned if he did, damned if he didn't type of situation.
By announcing his retirement he explained his lack of appearances, but gained criticism for his apanage.
Had he not announced it, though, and he would have been criticized for his lack of appearances, particularly in regards to events that QMII would typically be escorted to. It seems to me that Prince Henrik was already receiving criticism of this nature prior to the announcement of his retirement.
I would add that I think part of PH's problem is that he seemed to have taken a degree of resentment towards Denmark prior to his retirement (and via versa), and since his retirement has lived a somewhat extravagant life, while still taking an income from the Danish state.
I don't know much about Queen Ingrid, but if she was better liked in Denmark and lived a less extravagant life, I suspect the issue of her apanage might have been viewed differently had an official retirement been announced - the fact that she was a Dowager instead of a Consort likely would have helped too.
I think there's a good contrast between the retirements of Prince Henrik and Prince Philip; both are elderly men who immigrated to a new country and married women who became Queen. Both had to adapt to being "less" than their wives while also being expected to serve their adopted countries, and both in time are going to be beneath their sons (if they live long enough). Yet PH's retirement is poorly received, while the DoE's so far is largely well received. It's interesting, but I think it's largely because of the differences in their overall attitudes; the DoE got over being beneath his wife, and has been treated fairly well terms of being "beneath" his son (he isn't actually beneath Charles at all while the Queen is alive, and doesn't typically attend things where Charles is the Queen's representative), and has served Britain and the Commonwealth with a clear sense of duty. I doubt his wage will be reduced immensely when he retires, but I also doubt he'll be shown as living extravagantly after either - Balmoral, Windsor, and Sandringham may not be cheap to maintain, but it has a different appearance than a foreign vacation does.
The problem with PH is that he on at least two occasions were not there beside QMII when it was very much expected of him to be there. (The same thing would be expected by any other husband IMO).
His embarrassing insistence on being made king, in a culture where titles are not considered important, made it worse. Because PH was actually popular as never before just three years ago.
- Especially since he could not be made king, period. The politicians and the public was against it, and it would take a change of the Constitution as well, something no one is willing to do at present. Because constitutionally speaking QMII is a "female king". The wording in the Constitution refers to "the King", not the monarch.
Queen Ingrid was actually pretty unpopular until WWII and the Occupation, later on she became immensely respected. Respected rather than loved, mind you. But no one were ever in doubt that she was firmly behind her daughter, QMII. She fully accepted her role as supporting royal after the death of Frederik IX. And her devotion to duty was never questioned, even to the very end.
In contrast to PH, the DoE worked hard until he simply had to give up. He has AFAIK always been by QEII's side when needed and when expected and he has always been firmly supportive of his wife, despite his wit. He has never asked for a higher title than the one he has and he has again AFAIK never put himself before duty.
So the sentiment in Britain and the public opinion here in DK as well, as far as the public cares, is that the DoE has fully deserved to retire. That's the same sentiment expressed in regards to QMII. That she has fully deserved to retire, i.e. to abdicate - and because M&F are seen as ready to take over.
PH retired because...? Poor health. He would have been showered in sympathy if that was the case. But he seems to be in reasonable working order. Certainly able to travel extensively. - So why can't he support his wife on a few occasions?
Old age then? - Fair enough. He wants to enjoy the remaining years of his life. Fine, but why should he retain a full staff and a full apanage? These are money QMII can use, or M&F since they are stepping up their duties.
We have discussed many theories as to why PH retired. The theory that at present seems most likely to me is that QMII took him on his word when he probably had yet another fit about not becoming king. So he ended up "retiring himself out".