This is largely speculation, but based on canon appearances:
Vera may have been ill-suited for killing Reavers
All guns are not created equal, and not every task will call for the same kind of gun. Oftentimes there's a "good enough" margin, but sometimes that's simply not the case. Especially when fighting sci-fi hordes, some weapons are largely ineffectual. (A good example of this is the tactics used by the US Army during the Battle of Yonkers in World War Z : the firebombing, napalm, and chest-shots were utterly useless against a zombie horde.)
We don't see Vera used very often, but the main time Jayne uses her onscreen is during Our Mrs Reynolds, when he uses it for a long-range shot against a mechanical target.
It's very possible that, when confronted with an endless horde of Reavers, Vera simply wasn't the best tool for the job. Maybe she required reloading too frequently, or wasn't as reliable as some of the more rugged alternatives. Maybe her rate-of-fire wasn't right, she had high lethality but low stopping power, or he didn't have as much ammo as he did for other guns.
We'll never know his specific reasoning, but it seems that Vera was good for long-range shots against armored targets, but possibly not the most efficient gun for mowing down crowds of unarmored fanatics.