Paresthesia is the term for "falling asleep" so check that article out as well.
There are numerous reasons for peripheral neuropathy. You can google Wikipedia's article peripheral neuropathy for a long list of possible reasons. I used to have "falling asleep" issues with my arms and legs. I'd wake up freaking out as it took ages to shake feeling into my limbs. I thought I was sleeping in a wrong position but actually it was due to vitamin B12 deficiency.