It may or may not be a problem with the fuel pump or fuel system itself. You may be experiencing an electrical problem which only occurs when the body shifts such as when making a turn. (just a thought and I have seen it where a connection was corroded and when the body shift occurred, it was just enough to make that connection non conductive.) I see alot of other posts about the Neon losing power or stalling completely while taking a turn. Personally, I think the problem may be something bent/broke within the assembly inside the tank as you stated that the problem seems to arise when you're at or below 1/2 tank and non-existing when above 1/2 tank. I'm curious to see what the answer is to this one as there are so many different remedies to what seems to be the same "problem". I always replace the entire unit and never just the pump. One reason for this is it's a faster repair time. Another is I've never had any problems with the install where as I have with just replacing the pump. (usually the pump itself since it was aftermarket.) A complete assembly runs around $220. HEY!!! NO CRAP!!! You're from Saratoga Springs too huh??? If you need a hand let me know. I'm willing to help ya out if need be.