Narrative:

Flight to ZZZ; thunderstorms in ZZZ. Took as much fuel as ATOG would allow. Checked in halfway with dispatch; was told weather had moved through. Entering florida; we got a route that took us in big loop to approach ZZZ from the south. Sent route to dispatch; was told weather was building again; two alternates; ZZZ1 and ZZZ2. Got holding prior to ZZZ. Weather looked terrible over ZZZ; no way to get through to ZZZ1. Clear to ZZZ2. ATC was saturated. First officer got a word in about making plans to divert; ATC took it as immediate divert; gave us priority. This was fine; weather started building in ZZZ2. Told dispatch was diverting to ZZZ2. Set up for ILS (visual conditions); then ATC changed runway due to new thunderstorm. Set up for new runway; far too high due to ATC change. Tried to get down; got hit by +20 airspeed shear. Another carrier went around in front due to windshear. We weren't going to be stable; so went around. [We] came back in for second try. Another airline went around due to conditions in front of us. Visual conditions until very short final; [were] huge downburst and windshear; not safe to land. [We] went around. Departure said ZZZ was now better than ZZZ2. Still had 6.5 gas; went to ZZZ. Told dispatch. Set up for 10L ILS; shot approach. Short final; tower called 3;000 RVR due to heavy rain; below minimums. Lost sight of the runway and went around. [We were] informed that ZZZ1 was now 'light rain;' diverted to ZZZ1 with 5.2; shot visual; landed.I guarantee I made mistakes in diversion planning; approaches and missed approaches. ATC was nothing but helpful; but we were operating with incomplete information. Tighter coordination with dispatch and ATC; unfortunately; both were saturated. Our onboard radar was not useful; just showed red without enough resolution to find best route. Dispatch was trying; but there were diversions everywhere. They weren't much help in picking good diversion plan. ATC helped a lot; but their choice of runways didn't work. Luckily; I started the diversion with enough fuel to have choices.' fast-building thunderstorms cut off both alternates and required multiple missed approaches.

Related reports:

Google
 

Original NASA ASRS Text

Title: B737-700 Captain reports multiple missed approaches at two airports due to weather; finally landing at a third with less than 5;000 LBS of fuel.

Narrative: Flight to ZZZ; thunderstorms in ZZZ. Took as much fuel as ATOG would allow. Checked in halfway with Dispatch; was told weather had moved through. Entering Florida; we got a route that took us in big loop to approach ZZZ from the south. Sent route to Dispatch; was told weather was building again; two alternates; ZZZ1 and ZZZ2. Got holding prior to ZZZ. Weather looked terrible over ZZZ; no way to get through to ZZZ1. Clear to ZZZ2. ATC was saturated. First Officer got a word in about making plans to divert; ATC took it as immediate divert; gave us priority. This was fine; weather started building in ZZZ2. Told Dispatch was diverting to ZZZ2. Set up for ILS (visual conditions); then ATC changed runway due to new thunderstorm. Set up for new runway; far too high due to ATC change. Tried to get down; got hit by +20 airspeed shear. Another carrier went around in front due to windshear. We weren't going to be stable; so went around. [We] came back in for second try. Another airline went around due to conditions in front of us. Visual conditions until very short final; [were] huge downburst and windshear; not safe to land. [We] went around. Departure said ZZZ was now better than ZZZ2. Still had 6.5 gas; went to ZZZ. Told Dispatch. Set up for 10L ILS; shot approach. Short final; Tower called 3;000 RVR due to heavy rain; below minimums. Lost sight of the runway and went around. [We were] informed that ZZZ1 was now 'light rain;' diverted to ZZZ1 with 5.2; shot visual; landed.I guarantee I made mistakes in diversion planning; approaches and missed approaches. ATC was nothing but helpful; but we were operating with incomplete information. Tighter coordination with Dispatch and ATC; unfortunately; both were saturated. Our onboard radar was not useful; just showed red without enough resolution to find best route. Dispatch was trying; but there were diversions everywhere. They weren't much help in picking good diversion plan. ATC helped a lot; but their choice of runways didn't work. Luckily; I started the diversion with enough fuel to have choices.' Fast-building thunderstorms cut off both alternates and required multiple missed approaches.

Data retrieved from NASA's ASRS site as of July 2013 and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.