If it is under warranty (which if you bought it new, I think it is), call Uniden's tech support phone number. Probably faster than email. (And while Uniden *might* not be responding to your email, consider also that they may have not received it or you may not have received their reply. Recent tests of email at a variety of ISPs show that many are just silently losing up to 50% or more of messages. Overzealous spam-filters on either end can cause problems, too. I work in high-tech but I'm generally inclined to pick up the phone.)
I had a similar problem and they repaired mine quickly though they erased the programming back to factory settings so do a back-up first. They did offer to reprogram it for me but I didn't have a current list of settings.
If it is not under warranty then go ahead and try to fix it yourself before sending it in. Here's what I found when repairing the same symptom on my 396. The earphone jack is a surface-mount component at the top of the printed-circuit board. For low-cost and small size, this is good. For mechanical isolation it is bad as it is pretty much mounted in place by the solder connections. Get the earphone cord hung on a doorknob, yanked by your toddler, etc. enough times and you will crack the solder joints. This seems consistent with your description of it working for a while after you fiddle with it. The 396t isn't mil-spec or "industrial-grade" (but it doesn't cost a few grand, either).
Pull the unit apart and look carefully with a magnifier (I use a jeweler's loupe) and bright light. The cracks can be difficult to see. Alternately, just assume they are cracked and reheat all the joints with a small soldering tip. I was, after some searching, able to see the cracks. After resoldering, everything worked fine, again.
After repairing the solder-joints, I wiretied the earpiece to the base of the antenna leaving about a 1cm loop for strain relief and to be able to unplug the earpiece when necessary. The cord has been snagged and yanked many times since but no more problems.
The batteries are in series and rearranging them will have no electrical effect. The act of opening the battery compartment and removing/replacing the batteries could physically twist/shake or jostle things causing a weak joint to shift. On dry days I can definitely hear static buzz and hiss in the earpiece when I pull on a coat but that is the sound of the static disappating through the earpiece wire - it doesn't build-up somewhere.
