My take is that the limiting factor will not so much be the facilities (both Shipyards and Construction Decks should be fine for the job), but the technicians and the skills needed. An annual maintenance is probably going to involve all sorts of specialised procedures like jump field emitter tuning and sensor array realignment and superconductor fault proofing and so forth, which require special training to do, and people with special training are both expensive and difficult to find.
Going back to the original question about what it means for SDBs in systems without shipyards, it depends on what scale of operation we’re talking about. The very largest ones, such as the Imperial Navy or the megacorps or the like, will have their maintenance operations located at central depots and probably just use jump carriers to rotate SDBs in and out of their deployments as needed.
Smaller regional powers might do the same thing on a smaller scale, or they might have a dedicated maintenance ship travelling around to systems with SDBs, depending on the strategic circumstances.
Where you might have a problem, though, is when you’re a tiny, one-system power with just a few old SDBs. You could of course still hire the techs required and build up that capability, but if you only have a handful of ships that need an overhaul once a year, those people are going to sit around for the rest of the year and either sit around doing nothing or at best do other work that they’re significantly overqualified and overpaid for. Or maybe you could subcontract it out, but that’s still going to be expensive, plus then you’re depending on an outside organisation that might prove unreliable. So if the budget is tight, it might make sense to just save that money and hope for the best.
(Unless of course you're a tiny, one-system power like Torpol that happens to be sitting on a large trade route and gets a lot of civilian traffic, or one like Drinax that has an expansionist agenda and wants those capabilities for strategic reasons.)