B737-800
Flight Crew Air Transport Pilot (ATP)
Aircraft Equipment Problem Critical; Inflight Event / Encounter Fuel Issue
Flight Crew Landed in Emergency Condition
Aircraft
While level at FL370; both 'LOW PRESS' lights in right tank began to flicker; eventually staying on continuously. Ran appropriate QRH checklist. All engine indications and fuel quantities were normal. Contacted Dispatch and conferred with [Maintenance]. Based on conversation and normal indications; decided to continue. During descent; at approximately 22;000 ft; the right engine spooled down. [Advised ATC] and began turn towards [destination]. Engine restarted on its own shortly after we began our turn. Engine ran normally until maneuvering to final when it again spooled down. Ran checklists as appropriate and landed uneventfully. Taxied to gate and deplaned the passengers. At the gate our fuel indicated 3.19 [in] tank 1 and 4.28 [in] tank 2 at gate arrival. Total FOB 7.5. Prior to departure during the before starting engines checklist release fuel was verified at 26.4. In-flight fuel logs were kept and all checks were normal. Maintenance logbook entries were completed.
[Report Narrative Contained No Additional Information.]
B737-800 flight crew reported right fuel tank 'LOW PRESS' lights illuminated and right engine spooled down and restarted several times during descent and landing.