It’s possible that you are sleeping through nocturnal erections. They occur during rabid eye movement sleep (REM); since we experience REM more often in the last 3 hrs of the night, this is why we wake to morning wood. You may have a different REM sequence or wake from REM so slowly that the last of the series of nocturnals has already subsided.
Try taking 1 gram (1000 mg) of L-arginine 3 x a day, the last gram at bedtime. L-a often takes a week or more to kick in, but you are likely to see a difference in your nocturnal erection pattern after some use. Possible side effects: diarrhea and gas but this usually goes away completely in a week or two. If you tend to get cold sores and take much more than 3 grams a day , the L-a may cause them to happen more frequently.
There is a simple test for this called a RigiScan. Your urlologist will provide you with a little machine you can hook yourself up to. It will record the frequency, duration, and hardness of sleep erections. As you age, nocturnal erections become more and more important since they perform the “housekeeping” tasks of maintaining good penile health.