I do not really understand the logic behind the idea that Garp was an Admiral and became Vice-admiral because either he was getting older either he had done problematical things.
First of all, do you really think that demoting an Admiral to a Vice-admiral could be called a demotion ? The Vice-admiral position stay one of the highest rank of the marine ; that means Garp would have still got a special position in the marine (a seat in the " marine nomenklatura ") and thus he would not have been deprived of his officer rank and his freedom/power in the organization. So, that idea is not realistic as that is not what a demotion truly is.
Secondly, knowing that Sengoku said himself that if Garp was not the hero of the marine, he would have took responsibility for his family's actions makes me think that Garp never had serious problems with the marine/WG in his career. The fact that he is the hero of the marine has always protected him as Sengoku underlined it.
Now, about the idea that he became Vice-admiral because he was getting older, I do not really think it is plausible either. Garp stays one of the strongest person in the manga and some of us - mangahelpers'members - think he may be as strong/stronger as/than some of the admirals. Thus, why would he become vice-admiral : he still has the strenght to deal with almost any kind of situation ? Besides, it does not really seem fine to thank an Admiral by making him a Vice-admiral. I guess the marine would have created a special rank for the ex-Admirals if they were not the strongest anymore but enough strong to continue working for the marines as one of its strongest soldier.
And from what I know, an officer that retires keeps his former rank as a title. So, Garp would keep a vice-admiral title if he retired whereas he used to be an Admiral ?
That does not seem realistic either. I do not remind any story in our world about officers being demoted because they were old.
The most serious idea would be that he never got the admiral rank because of his behavior.