Truthfully, from your descriptions, it could have a few possible causes. I usually like to recommend the least expensive possible causes first. You know, the ones that just take some time and diagnosis? Then, move on to possible bad parts issues and the testing required to determine them.
So, that having been said, do a few of these checks first and report back. Then we can go further from there if necessary.
1) Pull the battery connection covers back and carefully look at both the positive and negative cable ends. Is there any corrosion on the connectors? The battery posts? The cables themselves, under the wire covers? If so, remove them and clean them up well and apply dielectric grease before re-assembling.
2) Follow your cables to their engine and fuse relay connections and review the connectors, posts, and wire conditions there. Clean as necessary.
3) Have you ever replaced your fuel filter? If not, or if not within 15,000-20,000 miles, do so.
4) Observe more carefully the conditions when it cuts out around corners. Is it just when you have 1/4 tank of gas or less? Detailed information will make it easier for us to try and help.
Report your findings back here.
Mike: 1997 SE w/ 183K, aka White Horse
, Gutted Airbox w/K&N, drilled 180* t-stat, tint all around, clear corners w/SilverStars, "PONTIAC" light up tail, PEMs, NGK TR55s