Is she imagining it

Hmm... suggest either she keeps a diary for a week and then confronts him or she confronts him ans says she is NOT imagining it and whilst she does not want to live in his pocket she would like to share some time with him & unless he can give her a reason why he does not want to agree tea/dinner every day plus x & y doing something each week . Then she should join a few clubs /start new hobbies and get on without him unless you think
a) he is depressed in which case he needs help
b) he wants out of the marriage..in which case your sister needs your support.

Does not sound happy whatever the cause.

She tried that yesterday at my suggestion and he sat with her for all of 10 minutes and then went off...

Could she ask him to come and sit with her to watch a particular TV programme or something? Then if he declined she could say that she misses sitting with him sometimes...and see what his response was??

But I have actually seen him do it myself

Yes she has asked him but he just denys it and says she is imagining it

Has she asked him why he's doing it, cheelu?