on = continues?

The expression is to "soldier on" and yes, it means "to continue".

It has the meaning of continuing despite some difficulties being encountered.

Defence cuts means reduction in the military budget.

Thanks

Also the phrase "soldiers on" is especially apt for an article about the military. Lazy journalists are fond of this sort of thing, so that an article about high achievers in the Air Force might well mention "high flyers", and an article about a promising and uncomplicated future for some project with naval connections might bring in the phrase "plain sailing". A drug company might need an "injection" of capital. You get the idea.

Interesting.