I'm afraid our special ministry, set up to pray for the people who get embarrassed when other people offer to pray for them, hasn't been massively successful.
I know it sounds an odd scheme. But it can be an odd kind of nuisance. There are people who simply don't want other people to pray for them. Not talking here about the normal, within a sensible definition of mutual boundaries or friendship, praying. More the kind of guerilla praying where people unexpectedly start offering to pray for you when you didn't actually ask for prayer. Normally - maybe nearly always - out of a desire to help combined with a certain relational clumsiness. But occasionally, you suspect, out of the desire to know a bit more. Or even in a cunning power-grab. "Let me pray for you/this situation", in a situation where the pray-ee is actually in disagreement with the pray-er, can sound awfully like "we're going to have to escalate this. But don't worry, I'll put God in the picture for you."
So I reckon people are just too shy to admit they need us to pray for their struggles with people who pray for them.
There's only one thing for it. We'll have to approach people we think have this problem. And tell them we are going to pray for them.