Put him to bed later anyways. Try 8:00 to 8:30., or when he starts to show signs of tiredness.. It may take him awhile to adjust, but he may come around and eventually get another hour of sleep in the morning, or take a short morning nap. The typical amount of sleep a child his age need is between 10-13 hours, so he is in a healthy sleep range, as noted here:
http://kidshealth.org/parent/general/sleep/sleep.html#
Here are some good sleep tips that may help with the nap:
http://www.askdrsears.com/html/7/T070100.asp
I have never heard of a weak immune system=poor naps. I know sleep is important for building healthy white blood cells that strengthen the immune system. There would be other signs though if this is the case, not just not wanting to nap, so here's some info on it:
http://www.suite101.com/content/signs-of-a-weak-immune-sy...
My kids grew out of naps around this age as well.