If the fuel pump stays on when engine is off that will drain your battery for sure, The problem is usually a bad fuel pump relay — the switch that controls electrical flow to the in-tank pumps. Under normal operation, the relay allows power through to the fuel pump only while it is running because otherwise they would RUNNING all of the time. But if the relay jams, "it may make your fuel pump run even when car is not on and draining juice from the battery over time." Some techs caution a bad relay can drain a car battery in 24-48 hours, especially on vehicles with high-amperage fuel pumps pulling over 10 amps.
Internal electrical shorts, in the fuel pump itself are another source of battery drain. Old pumps or ones exposed to debris and moisture can short out, drawing power from the battery around.... While an average fuel pump operates at 12V, malfunctioning ones may draw erratic amps — meaning they could be needlessly sapping extra juice just to function. This electrical drain will, over time destroy your battery and then you are that guy/girl who needs to the AAA or neighbour with jumper leads every morning. for extreme cases it can kill a newly changed battey in hours of common use from full charge it gets down so low starting car wont be possible anymore
This feel only exaggerated in colder climates. This can cause the alternator to have a tough time charging up a battery that is only half full of charge due to colder temperatures making it difficult for the battery itself from getting energy back. Cold-start problems further burden the battery, because a running fuel pump in an already hot car makes the situation somewhat worse. In areas where winter temperatures are below freezing, fuel pump issues have been shown to reduce battery life by up half due the extra electrical load and reduced cold temperature capacity of a lead-acid battery.
Regular maintenance checks can catch these problems early on. It can be tested for proper relay function as well as electrical integrity of the fuel pump by any technician. Using an ammeter to check current draw of the fuel pump when engine is off easily point out if that was the problem. Mechanics typically advise changing aged relays every 60,000 to 100,000 miles due to the fact that they progressively wear and also are a lot more likely with time to continue functioning improperly.
Automotive engineer Carroll Shelby was known to say, “Reliability is as important as performance,” and this axiom holds true with fuel pump maintenance too. A Fuel Pump that is good and has a relay operating can help stave off excessive battery drainage, as well allows the vehicle to be able to start. Acts such as these is what not only safeguards the fuel pump but also secures the battery and other components in order to have an overall reliable car.