Ok Judith. Don't want to derail further. It was the bit about 'extra spending money to treat herself', really does sound like it's on top of 'the housekeeping'. 
I think 'small gestures' are lovely in a fundamentally healthy relationship (in a bad one they make things feel even worse and I should know). But first of all you absolutely have to be able to talk about the big things. Sex is a big thing. She fobs him off with excuses. He can't second guess why she isn't interested, she needs to tell him, doesn't she?
Yes, she may feel like shit after having small children (been there with the traumatic birth injuries) but she won't TALK. I still think she seems to be the one with the problem. Yes we are hearing it from his perspective but he does sound like a pretty decent partner. He certainly gives a shit, just the fact that he's even on here suggests that.
The main problem is communication... without that gifts, tokens of 'appreciation' are like rearranging the deck chairs on the Titanic. Not that any woman who stays at home with kids wouldn't appreciate time away from them, to herself.
The OP is at a stalemate because, fundamentally, he can only guess what his wife thinks and feels. Look at the title of the thread... he doesn't know what she's thinking because she doesn't communicate. In his desperation he wants to get some insight from other women.
But only she can provide the answers, every marriage is different.
Sex five times in three years (even my stbxdh and I managed it more often that that) and her treating it like a non-issue by not discussing it is seriously wrong.
But to try to be more constructive, OP, if she won't talk, have you considered writing her a letter explaining how you feel? I get the impression she doesn't really know and might be a bit shocked if you told her (another thing that suggests that finding some other way - any way - to communicate might be helpful).
Sadly my husband and I have managed to spill out our feelings and be frank with each other about where our marriage went wrong via email, since we split. We've both accepted some responsibility for it and can see with more clarity now where it went wrong. It's an awful shame we never managed to do that face to face but it always became too confrontational, or I got stonewalled. Too late now :(
You can't just bury your head in the sand about this OP and 'hope it will get better'. Intimacy is a difficult thing to restore once it is gone.