Military dwarves don't spar every chance they get, and their rates will vary. Some individual dwarves hardly ever spar, others do it constantly. Personally I have all my dwarves in individual squads, and only put them in squads when I'm deploying them in dangerous areas where I don't want them going alone.
Placing dwarves in squads can also be useful when you want to assign an option (like harass animals or on/off-duty) to many of them at once, or when you want to station them all or put them all on a patrol. Giving an order to a squad of 7 dwarves will give all of them that order, even after they've been removed from the squad and are individual soldiers again. Giving an order and then splitting them up into 1-dwarf squads can be very useful if you want all available units to get to an area ASAP, like when a bunch of goblins just ambushed your legendary appraiser or what-have-you.
Back to your problem though, though my initial advice is that maybe they're all just taking a break (it won't say they're taking a break, it normally just says 'Soldier' for their current job), but also double-check that the barracks is still functional. If they're off-duty, uninjured, there's a barracks, --and they aren't marksdwarves--, there's no reason they shouldn't be sparring every now and then. Markdwarves use archery ranges and wooden or bone bolt to practice -- unless they're bugged (usually from holding a sock or extra pair of leggings or whatever in one hand-- tell them to Dump the item and they should get back on track).