747,
The answer to your question is that hand flying is encouraged, to a certain degree.
No one will criticise you for wanting to keep your skills together by hand flying, but there are times and places for such things.
A good rule of thumb to start with is perhaps not to overload the PNF. If for example you have just come back into the London TMA after a 2 man, night Chicago it may be better to not hand fly from "top of drop".
In practice, most guys hand fly a bit of the departure and will disconnect the AP and ATHR (if they feel like it), once they are reasonably assured of a landing ahead. After all, a hand flown go around in an A340-600 is rather hurried. I have done one...
So, in essence: No dictator SOP's to say what you can and can't do. Only common sense and airmanship.
And not all our flights are heavy crew. In fact, many of them aren't.
Landings a month? Depends, but I seem to get about 2 or 3.