DA40 Flight Instructor reported a fuel pump transfer problem during takeoff resulting in a diversion. Reporter stated fuel transfer pump issues are 'becoming more frequent' with aircraft left outside on the ramp making them susceptible to water contamination in the fuel tanks.

Narrative

Fuel Transfer Pump Failure encountered shortly after departure out of ZZZ and in flight after flight maneuvers training. Both myself and student ran cruise flow and turned on fuel transfer pump; checked EIS page and discovered no fuel transfer was occurring. Annunciator panel never displayed message validating pump was on. Ceased maneuvers to run Fuel Transfer Pump Failure QRH Procedure. Emergency Fuel Valve was selected on per QRH and balanced our fuel for our landing into ZZZ1 Airport considering curfew was still active at ZZZ. Fuel never reached max imbalance. Followed FOM for notification to Maintenance and wrote up the discrepancy in the aircraft binder. Prior to our flight; our aircraft was hangered all night and was not left out on ramp; we did receive fuel from FBO and student pilot sumped all 3 points per the checklist; and the student was under my supervision during the preflight and sumping of fuel. Water was found in fuel but was sampled additional times and verified all water had been removed. Note: Aircraft had a previous squawk with the same issue; but was inspected and cleared back to service by maintenance. Aircraft was left at ZZZ1 per maintenance and we were delivered another DA40 by another instructor. Have heard that fuel transfer pump failures are becoming more frequent. Maintenance said that water in the fuel is being discovered in other aircraft that encountered the same issue. Maintenance remarked that aircraft left out on ramp and not hangered are more susceptible to water in tanks and could be a cause of this issue.