Obviously it's all a bit speculative as we don't know your CV or the roles you're going for, but..
Are you applying for roles in industry areas in which you already have experience?
To move into a technical manager role, I'd expect recruiters will want to see either experience at a more junior level in the same industry sector and a demonstration of progression, or actual experience as a technical manager even if not necessarily in directly the same industry area. Of course, if they get applicants with managerial experience and product/process experience then these will generally be the ones they focus on.
Views will of course vary between different companies, and in general I've found that smaller business are (perhaps unsurprisingly) a bit more flexible on such things.
Are you applying through recruitment agents?
If so, it is worth asking them for feedback as they should know their clients well (although appreciate this is an optimistic sentiment based on experience with many recruitment agents both as a candidate and a client ) - it could be that they are finding that there are already lots of candidates with QA/Tech manager experience or at least more direct QA-type backgrounds, so frustrating though it may be, getting some time in a more junior QA role onto your CV could be necessary.
Your CV structure/content could also have a bearing - I'm sure you've already considered as much, but make sure this emphasises the direct experience of the relevant aspects for the tech/QA manager roles, and also the key aspects from the hygiene and food service areas that are directly beneficial for this type of role.
Also worth checking what training you've got in place at present - at this level I think most would expect HACCP at Level 3/4, Food Hygiene at a similar level, VACCP/TACCP experience/familiarity, BRC experience/familiarity etc.