Need to top my tyres up and the tubeless valves won’t unscrew

Presumably I will need to remove the entire valve?

What’s the best way to stop this happening again?

Mine some times does this. I find that you can often get them undone by holding the main valve body with the key for tightening it and using a pair of pliers on the end. I have found the best way of stopping it is to give the valve a press to release a small amount of air before doing it back up. It also helps to rotate your wheel so that the valve is in the 9 or 3 o’clock position before doing this.

Pop the valve cores out, pop some new ones from a knackered tube in. Simples. They last around 6 months or so before they start becoming a bit annoying, so I always find myself offering to take peoples dead tubes off them and pop it in the bin for them during rides so I can grab the valves.

A bit of silicone grease on the threads should help aid future removals

It happens – just replace the cores every now and again

10 cores for £11:
http://www.chainreactioncycles.com/Models.aspx?ModelID=20341

Vaseline on cores works well.

I was stuck on the trail with a puncture and no pliers to do this.
I found if I pressed hard on the top of the valve with the valve cap, it loosened it enough against the rim to undo it.
(Not all valves have removable cores folks).

I done a pic

Have just realised OP is talking about cores. Why not just pop a section of bead off to top it up?