My daughter's 240 sputters and dies when it gets down to just over a quarter of a tank of gas. Seems to me I've seen other posts with a remedy to this problem. No other problems or symptoms until the tank empties to this level.
Are there any visible damage to the underside of the tank? I have seen a gas tank with a large dent on the underside which caused some unusual fuel readings at empty.
The other thing I can think of is perhaps the piping or rubber tube between the filter and the in tank fuel pump have cracked and as the fuel level drops the in tank pump feeder tube is no longer submerged in fuel.
This would require you to remove the sending unit from the tank to check.