Not likely. Check the fuel pump ballast resistor and make sure the connections are tight on each end of it.
Do you have a multi-meter?

No, Crusier, I don't have any kind of meter, but can either find someone with one that knows how to use it, or can borrow one and figure it out with a little help. What should I look/test for? Seems like if something like this was loose, then the "short" would go both ways. Right now it drains slowly, but comes back quickly -(if it does at all) never drops or drains quickly. Because of that aspect of the symptoms, I've never really thought it was anything loose, in the traditional sense. I keep thinking the fuel pump itself (and what a pain that'll be to replace, for a guy that doesn't like working on cars, but can do it when needed), or the PCU (or whatever it is called computer thing) which looks much easier (though more expensive) to replace. Time, or money? Not sure which I'm in favor of spending more of right now...

I do have a (mostly) minor fuel or exhaust system problem, but it never seems to coincide with this problem, so I've never put the two together. I've mainly suspected it to be an exhaust problem, though, as it seems to hesitate, or get plugged up (like a catalytic converter that is near its end). But I suppose it could be a clogged fuel line. I admit to not replacing the line between the tank and the filter when I replaced the filter, so, maybe that might be the problem that is causing both things? Might just replace that line and the filter again, see what happens. Relatively cheap and easy enough to do, and couldn't hurt anything.

A decent little digital meter can be had for under $15.

My Jeep cherokee has low voltage. Good strong battery, new altenator. does my ECU control voltage regulation?

Its a 1991 With a 4.0Liter HO

Yes on a 91.