If you have been running your vehicle with low fuel levels frequently, it is possible that when the fuel pump gets hot it will stop working until it cools off. The gasoline actually keeps the fuel pump cool and makes fuel pumps last longer. You may have to replace the fuel pumps to fix problem. This issue may also be caused by a faulty fuel pump relay(found under hood in fuse box).
RepairPal Certified shops can diagnose and repair your 1999 Buick Regal. They provide transparent pricing with a minimum 12-month or 12,000-mile warranty on repairs and services.