B737-700
Flight Crew Last 90 Days 221; Flight Crew Type 13500
Inflight Event / Encounter Weather / Turbulence; Inflight Event / Encounter Fuel Issue
Flight Crew Executed Go Around / Missed Approach
Company Policy; Weather
Flight to ABQ was uneventful; though very bumpy in the descent. We broke out at around 11;000 feet and it was VMC below. The ATIS was calling winds around 210/10. We were cleared the visual; but flew the RNAV Y 21 ground track for lateral and vertical guidance. We configured and turned base. We were cleared to land and the winds were then reported at 180/7G45. Shortly after the wind report; we received a PWS warning 'go-around; windshear ahead.'  We went around with Tower. Tower gave us a climb; and a turn to the west; and had us contact Departure. We checked-in with Approach; and they asked our intentions. We checked on the field conditions. We were told things were calming down. We said we would try again. It also sounded as though another aircraft was going in front of us. We configured and turned base again. The winds were reported at 210/7G45 (what happened to calming down!). Once again; we received a windshear warning. (In all truth; neither the First Officer (FO) nor I are sure whether the second one was a GPWS warning or a PWS warning). We went around again.  Now we were less than 4;000 pounds; with a low fuel warning. I ran the Low Fuel Checklist; and declared minimum fuel.  We quickly looked for AEG (Double Eagle) information on the flight computer or in the Jesppesen Approach section; but discovered there was no info available. Meanwhile; Approach said the winds were continuing to swing around the west and were now 280/7G45.  They were offering to change runways as the microburst had moved north and the wind was swinging West/North.  We slowly swung around to land on Runway 3. By the time we were configured and cleared to land; the winds were called 280/7; with the Southfield winds calm.  We landed on Runway 3; and shut down with 3.3.The plan showed forecast winds gusty down the runway and calming to 10 knots for arrival.  No talk of TS; CB; or windshear. The 5.3 arrival fuel was legal. However; our closest alternate would be Roswell. Divert fuel is 3.0. Followed by ELP; at 4.0. KAEG and KSAF; though available pieces of concrete; are not in any of our 'books.'  We had a plan; and it involved landing at Double Eagle; if the final approach didn't work; but it is not a plan I liked. I accepted 5.3 arrival fuel.  That is just not enough with no good alternatives around.
B737-700 Captain reported landing with 3;300 lbs of fuel after two go-arounds at ABQ triggered by windshear warnings.