My advice is to move nap time forward. My daughter wakes anywhere between 6:30-7:30 in the morning. Her nap is at noon. I tried pushing it back to 1:00 and she skipped many naps! I then moved it forward to 12:30 and she would still skip. Once I moved it to 12:00, she has skipped two naps in two months. I would love for her to nap later in the afternoon to give us more time at playdates and such, but right now she is stuck on her 12:00 nap.
So maybe you can try putting him down at 1:00 for a nap, if he still doesn't sleep, try 12:30, etc. I think he's overtired by 1:30 and thus not sleeping. Though its weird that he goes right to sleep when he does nap and not when he skips a nap. My DD is the opposite. The days she misses a nap, I am guaranteed for her to fall asleep in 3 minutes and the days she doesn't nap, it goes from 45 to 1.5 hours to get her to sleep!