Studies have shown that total and partial sleep deprivation can increase pain sensitivity. Dr. Roehrs et al did a study published in the Journal Sleep, in which they determined whether an extended bedtime would increase alertness and reduce pain threshold in sleepy individuals.
They enrolled 18, healthy, pain free but sleepy patients who most likely were sleep deprived. The patients were randomly selected to either continue their current sleep schedules or to extend their sleep upto 10 hours per night for four nights. The results showed that on average, those with the extended sleep duration had reduced sleepiness and reduced pain sensitivity. The study authors speculate that being sleepy can increase pain sensitivity. They concluded that reversal of mild chronic sleep loss improves pain sensitivity. They think that sleep loss could increase systemic inflammation, which could increase the sensitivity to pain.
I'm not sure what these results mean for clinical practice. In my experience, chronic pain patients have chronic insomnia from various reasons - pain, certain medications for pain, and inadequate sleep hygiene. Sleep deprivation is not usually present and these chronic pain patients couldn't sleep any more. Some chronic pain patients are sleepy during the day, but not from sleep deprivation, but from the pain medications.