There are several issues to consider before "press-ganging" your archers:
1) A volunteer field party is motivated, friendly and provides a good ambience. Archers who have been told to turn up or lose membership can be surly and spoil the atmosphere for everyone
2) Where I've seen rotas used, they've been a massive flop - whether for field parties or for beginner sessions, your club has archers who are there for the social element and hardcore competitors, who (even if they're really engaged in the club) sometimes need to get on with training and your competitions should be to help them get good scores.
3) It's too easy to go "I'm sorry, I can't help out that day". If pressed further the message will become clear: "---- off".
4) It's also too easy for your serious archers to leave the club if they don't feel welcome - that's the last thing we want.
There are others, but these certainly spring to mind.
Instead, consider why you have always the same few archers. This can require asking some pretty unpleasant questions...
1) Is the "field party" element of the club a bit of a clique? Are they all from a certain background, age group, locality, do they all socialise together when at archery, go to the pub together afterwards...? If so, this must be dealt with before anyone will help out.
2) This is easy if you don't actually want a clique running your club - most don't but given the time most club committees have been running them it's all too easy a habit to slip into.
3) Celebrate the people who help with the field party, encourage them to share their enthusiasm with other members and make it clear that anyone else coming along will be regarded as a hero rather than an interloper or making up the numbers. Make sure it doesn't look like a "long-term members only" thing - talk to the parents of juniors for example - they can become very keen on making sure the club is well run.
Generally, when people don't want to help out it's either because they have other commitments or (more usually) because they don't feel that wanted, because they see the core of the club as a tight-knit group that would prefer to be left alone to do the running. Same reason AGMs and committee positions can be tricky to fill. Sad thing is, it's a vicious circle of self-fulfilling prophecy.
The good news is that it's easy to break by stepping outside your past behaviours - even just a little way.