It is normal for oil pressure to fluctuate somewhat along with engine speed. It may also decrease a little when oil is warm. The phrase "bottoming out" is frightening though. It should never go to zero.
If it is bottoming out there are several things that may be wrong. The worst case scenario is that your oil pressure is actually fluctuating as indicated by the gauge. If that's the case you need to get that fixed PRONTO! This could be caused by an oil pump on the verge of failure or "trash" in your oil filter, or more sinister problems deep inside the engine. Aside from the filter, none of these is easy to fix.
If it was my car I would purchase and install a mechanical oil pressure gauge. If the mechanical gauge fluctuates like the old one then the problem is actual oil pressure see paragraph above. If it's stable then it's the wiring or sending unit and you can breathe a sigh of relief. Try replacing the sending unit first. If that doesn't fix it then you'll have to chase down a wiring problem.
