Dispatcher reported communications failure with a company aircraft experiencing a bleed air system failure; resulting in the aircraft diverting.

Narrative

XA42z: Received ACARS from the flight advising of 'air sys 3 off' alert. I referenced the QRH to determine the consequence. #2 Pack already on MEL so the flight is down to 1 pack. QRH consequences; 'IF MANF FAILED DO NOT REPRESSURIZE; WING ANTI-ICE NOT AVAILABLE; NO FWD CARGO HEAT' I also referenced the MEL for operations with 2 packs inop. FL250 limitation in addition to the above. Contacted Maintenance Operations and asked them to review the ACARS and aircraft systems while I got further information from the flight. Checked with the flight via ACARS; they were able to maintain planned flight levels but had concerns about reaching U.S. if required to descend to FL250. Flight would be able to reach ZZZ or ZZZ1 at FL250 but we also had to consider possible icing probable icing conditions in those locations. Flight called in on SATCOM and I was able to conference in Maintenance to discuss any options the crew may have to cross feed manifolds or regain #3 sys. While they troubleshot the problems I asked to look at west coast including planned destination to see if we could operate non-icing. Response was entire west coast likely to have icing conditions on descent. Maintenance Operations / flight crew unable to restore the #3 air sys. Both Captain and I agreed that a return to ZZZZ or ZZZZ1 would be the safest course due to no wing anti-ice. Finally determined to return to ZZZZ1 with alternate ZZZZ. After initial SATCOM call; we were unable to re-establish comm via SATCOM. Call would drop as soon as the phone was answered. Continued comm via ACARS and eventually established a phone patch via ZZZ2 ARINC.