Date: 201901
Local time of day: 1801-2400
Location: ZZZ.Airport, US
Flight conditions: IMC
Weather elements / visibility: Rain
Aircraft: B737-900
Operator: Air Carrier
Operating under: Part 121
Mission: Passenger
Flight phase: Final Approach; Initial Approach
Airspace: Class B ZZZ
ATC / advisory: Tower ZZZ
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Not Flying
Reporter qualification: Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
Human factors: Fatigue
Second reporter function: Pilot Flying; First Officer
Anomaly: ATC Issue All Types; Conflict Airborne Conflict; Inflight Event / Encounter Fuel Issue; Inflight Event / Encounter Weather / Turbulence
Detector: Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance; Flight Crew Diverted; Flight Crew Executed Go Around / Missed Approach
Contributing factors: Human Factors; Environment - Non Weather Related; Weather
Primary problem: Ambiguous

Narrative: We were on the arrival and assigned a hold due to the weather at our destination. We held for 1 hour. All runways were closed and nil to poor braking was reported. After the 1 hour holding delay we were cleared for the approach to ILS10 C. The First Officer and I discussed the situation and our fuel status and our options. We confirmed our plan with dispatch and decided to continue to ZZZ. On the first approach; we were vectored off to give spacing with a heavy international 787. After a delaying vectors we were once again recleared for the approach. We were assigned a speed of 160 knots 15 miles from the runway. We complied. Approximately 1 mile from the field; the Tower instructed us to go around due to loss of separation. We went around and stated we were now in a minimum fuel state and could except no more delays. ATC vectored us back for a second approach. The weather had deteriorated more to 1/2 mile visibility and slush covered runway at reported depth of 1/8 inch completely covered. We opted to perform a flaps 40 Cat 2 autoland per the approach plate. On the second approach at approximately 300 ft. from touchdown; the Tower instructed us to immediately go-around stating the preceding airplane had slid off the runway. We performed a second go around and immediately diverted to ZZZ1. We were at our minimum fuel and decided that was the safest course of action. We did a 3rd low IFR ILS Autoland into ZZZ1 and it was uneventful. We contacted Crew Scheduling about what they wanted us to do. Their first plan was for us to refuel and fly back to ZZZ. We stated that we thought we were close to the end of our duty day. Scheduling then said that they wanted us to sit on the plane and wait for a possible inbound crew then deadhead to ZZZ. The First Officer and I discussed this and decided it was best to get some crew rest at that point due to the long and very difficult flight we encountered. We felt we were extremely exhausted and not functioning with very clear thought process and our communication skills were degraded. We decided that to layover at ZZZ1 was a safer option. We believed that continuing to work in an exhausted state of mind and body would not be beneficial for the airline.


Second narrative: ZZZ closed all runways for landing due to poor to nil braking action. We held in holding pattern for slightly over an hour; RIGHT when we hit bingo fuel and needed to divert; they opened up one runway for approaches/landing. We were the first aircraft cleared out of hold and to descend via RNAV arrival. On approach descending on glideslope; ATC decided there wasn't enough spacing between us and the preceding heavy and vectored us off approach to go back around to try again. We decided to give it one more try; and at around 300 ft. on 2nd approach; Tower instructed us to go-around; that preceding aircraft went off runway. At this point; we were min fuel and could not try again. [We were] worried that the runway would again close for awhile; so we decided to divert to ZZZ1. I knew the Captain had not slept well at all the night before and noticed he was at times slow to process some things; I myself also missed some things and didn't perform my go-around procedurally as well as I normally would. Parked at the gate we were pretty fried and decided it'd be best for us to call in fatigued.


Synopsis: B737-900 flight crew reported diverting following two missed approaches and then calling in fatigued due to the long stressful flight.