I don't know your exact setup, but the FP relay needs several inputs before it will keep the pumps on. For instance, it needs a signal from the ignition that there is RPM, so if the engine stalls it will shut the pumps off until the key is recycled.
The same signal that is missing from the relay may also be the cause of your rough running. You need a wiring diagram to look for the common point of failure.
Falls Church VA
'66 200, '66 230SL, '96 SL500. Sold: '81 380SL, '86 300E, '72 250C, '95 C220, 3 '84 280SL's '90 420SEL, '72 280SE, '73 280C, '78 280SE, '70 280SL, '77 450SL, '85 380SL, '87 560SL, '85 380SL, '72 350SL, '96 S500 Coupe