what pattern follows? when enable notifications and tweets notifications appears we are sorry and an message about problems of your connection?
i had same problem, but i had to start from zero
well please before please check the following
1) check in your settings or each @ be enabled the mobile notifications first
2) check if in background tasks are enabled twitter on the background tasks if is disabled please enable it
3) if nothing seems to work in the case please go to your twitter on your web browser and revoke authorization to all the twitter apps , , and when i say everything is everything.
4) later try of open the twitter app and log with your username and password and please enable the push notifications
and to everything say yes, is like absurd but later can change the lock screen
with this can solve the problem at least to me i solved of that way