I have this problem always especially after forearm training. Depending on how intense the training was my arms go to sleep 1-5 times per night. After a few days without training it doesn't happen anymore.
There are different reasons for your limbs (in your case arms) go to sleep, as you can read here:
In your case I guess it's because of pressure. Is it possible that you sleep on your arms? That happened to me a lot since then I try not to put my head on my arms.
An other possibility is a vitamin deficiency. While you train YOU HAVE TO EAT HEALTHY! I just don't get people who work out 4 times a week and don't give a sh.. about what they eat. Eating is half your work out people!
Hope you'll find out what it is exactly.