An E39 owner had it fixed by using a bottle of Techron Concentrated in the gas tank. Search for it in E39 sub-forum. It doesn't hurt to try.
01 Anthracite 525i Sport, 03 DINAN 540i M-Sport, 06 DINAN E53 4.8iS, 90 Straman Z32TT,
01 E53 3.0i and 91 Z32TT (Gone, but not forgotten)