Hi J., my son is just around the corner for turning 20 months and we went through something similar at 18 months... right after his 18 month check-up, too! For two weeks he started sleeping less at night (I think now maybe it was a result of the chickenpox shot he got that I was unsure of whether to give him at all). Anyway, because he started sleeping less at night, he was getting crankier and crankier with just one nap, and his naps were getting so short they were almost non-existent, so I went back to two naps (or one nap if he had a solid 12 hours the night before) and he was doing well with that for awhile. He just this past week started going back to one nap, but he keeps pushing it later and later and now I find that he prefers to go down even as late as 1:30 (he wakes up between 7 and 7:30 lately). For the most part, I have an idea in my head of when I'd like him to go down, but I just watch him and see how he is (or sometimes I try to put him down at a certain time, but he'll insist that he wants to use the potty or something and prolongs going down). Some days he seems really tired in the morning so I'll put him down for a long morning nap but then he refuses an afternoon nap, so I think he's ready for one, but he varies daily on the time when he's most ready for his nap.
I hope this helps you... or at least lets you know that you're not the only one dealing with a stubborn toddler!