I have had a couple of problems recently but these were solved with a redial and then it connected ok.
Have you had a look at the network info on the frontpage when it loads up?, that may give you a clue to any problems.
To be honest I think anytime is not too bad, but maybe thats just tempting fate !
The only ISP I would totally recommend to anyone is Pipex ok its £14 pm but you connect everytime and the service is great, but you have to pay for the calls as well , if they have any packages for 24/7 they would be the ones to go for.
I found a link that I think was previously on here for ISPs, it may be of use.
http://www.internet-magazine.com/isp/index.asp