"difficult to shake" is a correct and usable part of a sentence in written English. You can use it when you want to emphasize that something is hard to get rid of or that it has deeply affected someone. For example: "His feelings of disappointment were difficult to shake.".
For him, it's difficult to shake off the celebrity [tag].
It is difficult to shake off a greasy grilled cheese.
Each time I return, I dredge up memories that are difficult to shake.
Linguistic insecurities and peeves, once they take hold, are exasperatingly difficult to shake.
But the accusations were difficult to shake — even from thousands of miles away.
Ireland's pub culture is where widespread acceptance of smoking is more difficult to shake.
It's difficult to shake the feeling that time has stopped here".
Ludwig does not simply clarify my doubts with English writing, it enlightens my writing with new possibilities
Simone Ivan Conte
Software Engineer at Adobe, UK