Heu...
Queen Wilhelmina had no full support of the public in 1948?
Grand Duchess Charlotte had no full support of the public in 1962?
Queen Juliana had no full support of the public in 1980?
Grand Duke Jean had no full support of the public in 2000?
Queen Beatrix had no full support of the public in 2013?
I didn´t name Wilhelmina, Charlotte, Juliana or Jean nor Beatrix!
All these sovereigns are from monarchies with abdication-tradition (in fact, abdication became only and not before popular in the NL because Queen Emma, who originally was Queen consort, had to hand over the office to her daughter who became of age).
Both Belgium and Spain had no abdication tradition before (Leopold III also abdicated only because huge resentments against him for his role in WW2).
In the Netherlands and in Luxemburg this custom works; we´ll see how in the long run things develop both in Belgium and Spain. I only hope for the best of these countries!
Monarchs like Elizabeth II or King Harald who have been anointed or at least blessed by the church should never abdicate as this tie can only be dissolved by god, in my opinion.
Juan Carlos was also blessed (and anointed) in the Jerónimos Church roughly one month after his proclamation as king by the
Cortes. Although I respect your religious beliefs, modern monarchs (including Queen Elizabeth II) are not really kings/queens "by the grace of God", but rather by the will of the people represented in Parliament. Even in the UK, Parliament can depose the king or change the line of succession as shown in the cases of James II and Edward VIII.
I also think that an abdication tradition or lack thereof is not the real issue. The monarchies of Spain and Belgium are more fragile in comparison to those of, let's say, Denmark or the Netherlands because of structural problems in those countries, most notably Flemish separatism and the linguistic divide in Belgium, and long-term leftist republicanism, Catalan separatism, and, more recently, the economic crisis in Spain. Corruption scandals and other circumstantial controversies involving the Royal Family only add to those deeper, structural issues.