Is there a pattern to the signal "drop out" you experience or is it random - both in terms of regularity and duration?
Dead spots ... multi-path (reflections) .... poor signal strength, on the one hand, and/or poor connection on the other hand - the 2 most liklely causes.
2 things to try:
Relocate the antenna
Try is relocating your antenna mounting on the vehicle - make a journey and note down those spots/areas where you experience drop out, reposition the antenna and make the same journey again. It's quite possible that as a consequence of the change in ground plane geometry that occurs from re-positioning the antenna you may well exeperience a reduction in drop outs, or indeed an increase, but overall I suspect you're not likely to realise so much of a difference that its going to be worth while.
Poor Connection
The only other possible cause I can think of is a poor antenna/coax or electrical connection. You dont say anything about your BCD396T momentarily dropping out (as in switching off briefly, then switching back on - does the display momentarily go blank?), so if the "drop outs" are irregular and related to movement/vibration, theres a possibility you have a poor/loose coax connection. Continuity test with a digital multi-meter will quickly address that as the cause, if its the cause. Set things up so you can Manipulate/move/shake the coax/antenna around while testing - if theres a poor connection the multi-meter audio should breifly drop out. Do this with and without the Uniden connected - it's possible, if it is a poor connection it could be the coax connector on the actual Uniden.