B737-700
Flight Crew Last 90 Days 250; Flight Crew Type 15000
Time Pressure; Workload
ATC Issue All Types; Aircraft Equipment Problem Less Severe; Deviation - Speed All Types; Inflight Event / Encounter Unstabilized Approach
Air Traffic Control Provided Assistance; Flight Crew Overcame Equipment Problem; Flight Crew Executed Go Around / Missed Approach; Flight Crew Landed in Emergency Condition
Aircraft; Airspace Structure
ATC radio traffic was congested. We got a late clearance to turn to final from a high and tight position; requiring above normal aggressive aircraft maneuvering to land. During this; we had a system malfunction that caused stick shaker and airspeed low alerts which prompted an immediate go. The late clearance made it very difficult to quickly analyze the system problem. We returned to land several times as we diagnosed the system problem. On one of those approaches we received a clearance to land too late to make a safe approach; requiring a go-around. On our final approach and subsequent landing we notified Approach Control for a non-standard LE Transit Flap 15 procedure; only to be asked by the same Tower Controller who had given the late clearance to land about the souls on board and fuel state when we were below 1;000 feet on short final.  Very distracting again. Preventative measures: No day is perfect in the Tower or in the air. Late clearances to land from high tight positions do happen in the real world periodically and are not ideal. It just happened to occur during a serious system malfunction. Not really much to say about it really; but the later general aviation around caused very late clearance to land by other Tower Controller and subsequent querying us below a 1;000 feet on final regarding fuel and Passengers was excessive. These errors need to be reviewed with that Tower Controller.
We were cleared for a visual to 13R in ZZZ and given a high and tight vector. We started extending flaps and got a stall shaker; which prompted a go-around. We might have been able to identify the LE FLAP malfunction sooner had it not been for all the distractions from traffic; radio congestion; and ATC vectoring us in so tight. On one attempt; we resolved what we thought was an erroneous performance input. After an aggressive vector to final; Tower told us to continue; and then cleared an aircraft behind us to land. After some confusion on ATC's part; and a lot of radio congestion; we were finally cleared to land but we were below 1;000 feet; so we went around again. At this point we identified a LE Flaps Transit light. We asked for delay vectors and thoroughly ran the QRH for a Leading Edge Flaps Transit procedure; prompting us to execute a flaps 15 landing. As a precaution the Captain asked approach to roll the trucks. Approach told us that in that case he was declaring on our behalf and asked us fuel and souls onboard. Once we were stabilized and had all checklists completed; we were cleared to land. On short final; below 1;000 feet; Tower proceeded to ask us the very same questions as Approach had asked; to which the Captain told her that it wasn't an appropriate time for that. The landing was perfect and Tower apologized as we exited the runway. Preventative measures: ATC may want to consider not cramming an aircraft that had already gone missed approach back into the traffic pattern. Also; it would have been nice had Approach communicated the fuel and souls onboard information with Tower. In addition; it was inappropriate for Tower to be talking to us that late in the game; on short final; during a QRH directed flaps 15 landing.
B737-700 flight crew reported a leading edge flap failure during final approach.