Hi,
I have a 11month son (my second) and he's been toying with the idea of one nap a day for the last 3 or 4 weeks. I've gone with the flow and let him go without his morning nap, which was around 10am, after waking at around 6.30/7.00am. He's been happy to last until after lunch before napping again and then he naps for 2 or more hours. However, the last few days he's been wanting a morning nap again, the signs were that he was clumsy and grumpy so I've put him down again mid morning and got him up around 40 minutes later. It's worth looking out for those basic signs again such as eye rubbing too, as I think sometimes you get so set in a routine that you forget to watch for the signs your lo is giving you.
Anyhoo, my youngest ds is still napping for a couple of hours or more in the afternoon and he's not been affected during the night, thankfully.
My thoughts are that he knows his basic routine for the day and like any human he's more tired some days than others depending on what we've all been up to. He'll let me know if he needs more sleep or less sleep during the day if I take the time to watch - which isn't always easy with a toddler around too.
I agree that your lo is probably overtired and that's why there's a fuss at nap time. Do you find that they sleep better at night if they've slept well during the day or is that not the case?
I also have an almost 3 year old who doesn't nap anymore (except for occasional sleeps following a busy week or whatever) and he consistently sleeps 13 hours at night. I recently read that kids need a nap until around the age of 4!
My advice would be to listen to your child and see what he's saying about napping, and be flexible, he might want two naps occasionally until he's a little bit older.