Date: 201701
Local time of day: 0601-1200
Location: FAY.Airport, NC
Flight conditions: IMC
Light: Daylight
Aircraft: Medium Transport
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Flight phase: Initial Approach
Airspace: Class C FAY
ATC / advisory: Tower FAY
Aircraft component: FMS/FMC
Component problem: Design
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Not Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP)
Human factors: Situational Awareness
Second reporter function: Pilot Flying; First Officer
Anomaly: Inflight Event / Encounter Unstabilized Approach; Inflight Event / Encounter Weather / Turbulence
Detector: Automation Air Traffic Control; Person Air Traffic Control; 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; Aircraft; Weather
Primary problem: Weather

Narrative: This [report] regards two missed approaches to Runway 22 at FAY; and subsequent diversion. FAY METAR was for 9500 overcast; with a TAF of OVC 9500. However; when we arrived the ATIS was reporting 400 BKN. Approach in use was a Localizer Back course to Runway 22. We inquired if the ceiling had improved and [were] told it was 500 overcast. Minimums to runway 22 were 560 MDA (380 feet). As a non-precision approach we were required to round up to 600 MDA which should give us (420 feet) so 80 feet of ceiling to see the runway. We don't do a lot of Back Course Approaches; in fact this is my second in 2 1/2 years. The FMS was not cooperative; it auto sequenced even though I tried to inhibit; (I executed the inhibit too late); I reselected the approach; resulting in a late decent to 600 feet just past MORGY. I looked up to see our descent rate at 1300 FPM at 740 feet and deemed it an unstable approach and commanded the First Officer to Go around. As I announced our Go Around to ATC as they were simultaneously broadcasting a 'Low Altitude' alert; so our call was stepped on. ATC restated the altimeter; and asked us to check our altitude as we were climbing well above 1000 feet. I'm not sure if there was an electronic error on either part; but I recall having the current ATIS; and us not going below Minimums for the Approach. I'm not sure if the unstable descent rate triggered the alert; but knew that the Go Around was the right decision. I again announced the GO around to ATC which gave us a climb to 2000 feet then over to departure; who vectored us at 3000 feet for a requested RNAV (GPS) RWY 22 approach. Minimums for this GPS approach were identical; and again; ATC vectors took us through the missed approach hold; causing a re-sequence of the approach as we drove through the hold. I reselected and cleaned up the approach in plenty of time to shoot a much more stable approach. Level at 600 feet; the ceiling from the FAF to the field was at 400 feet; and finally rose to 600 feet over the runway numbers. We did break out with 4 bright white PAPI lights over the numbers; obviously too high to land safely. With two failed attempts to runway 22 at FAY; we elected to divert to our filed alternate. We refueled and with better weather returned to FAY which had turned around by now and gave us the ILS to Runway 4. The return and approach to FAY were uneventful.


Second narrative: [Report narrative contained no additional information.]


Synopsis: Air Carrier flight crew reported performing two missed approaches at FAY due to weather and an un-stabilized approach before diverting.