For normal midi useage, each note played should have a note off command, but drums might be considered 'not normal'.
All drum notes would come with a very specific envelope, which would force a note off regardless. However, a normal drum sound would usually reverberate into the next note anyway, this might be considered normal. You do sometimes see a drummer hit (say a cymbal) and then reach over to touch the cymbal to stop the sound else it would keep ringing for some time.
The designers of the device you have could have decided that an explicit note off is not necessary?
What is the multi-timbrality of the device, i.e. how many sounds should it be capable of playing at the same time? 32, 64, more? Do you feel that this is clogging up? How does the device respond if the limit is exceeded, if it does a first-on-first-off system this may be fine, but a last-on-first-off would be no good. It's unlikely to work on a no-more-when-full system, but if it does, that would be a BIG problem.
What does the manual for the device say about all this?