I would tend to believe that starbases would be situated in strategic locations where Hydrogen and its isotope, Dueterium, were present or close at hand. Starbases are important as supply depots, personnel transfer points, limited repair facilitiies and refueling points.
They also deny an enemy access to, say a gas cloud or gas giant containing star system.
Trawlers could collect and store the Hydrogen at the starbase for processing, unless processing was conducted in transit by the trawler itself.
However, anti-matter is something that has to be created and a starbase would not be able to house a particle accelerator capable of creating enough anti-matter fuel for a warship, let alone a fleet. CERN produces 3 to 5 anti-Hydrogen atoms a year. One would need a seriously big operation to produce industrial levels of anti-matter for MAM reactors.
Even starbases would require the occasional visit from a tanker to top up their storage tanks.
Rick Sternbeck proposed that the inclusion of Dilithium Crystal Focus, in order to control and regulate Warp reactors was the breakthough in Warp Drive (perhaps Kelso's reference to , "We've solved the time barrier" in "The Cage" could have been this) nush in the same way that the introduction of Quartz Crystal stabalisation was a huge breaklthough in radio back in the 1930's. Gene Roddenberry based a lot of the Warp Dynamics science on his wartime experience with aircraft radio during WW2. As a radio ham I see how Star Trek has Warp Drive physics and radio physics as one and the same.
As Warp drives become more effiecient obviously the ranges between refueling sessions would decrease. It a bit like Jets versus Tubo Props versus Piston Engines.
If one looks at the huge support fleets that the US Navy had running backwards and forwards between battlefleets during the Pacific campaign, one can't help but be impressed. Old destroyers gutted out and converted into fleet battle tenders (ammunition and spare aircraft), fleet oilers, repair, personnel and hospital ships, etc.
All of which enabled the US Navy to stay at sea for a longer than normal period and not have to resort to resupply at a port.
Both the Royal Navy and the Japanese Navy were dependant on extensive base facilities, which in themselves, proved vulnerable. Without an active base you cannot operate a battlefleet in an area for long.