I have always had problems with my websites that were mapped to certain folders on my shared hosting package, with connections being reset or timing out. This it turn out was due to the server my hosting package was being hosted on.
I had engaged with my hosting provider (123-reg.co.uk) before over this, but since it was never a serious problem and they provided information to improve performance, I never really pushed to get things improved.
After setting up a website monitoring service I soon noticed how widespread the problem was, with my sites performing badly and going offline every few hours, this of course could not continue. So I contacted the support of 123-reg and within a day that had moved my hosting package to another server which has greatly improved performance and I have not seen a single site failure since. I am very happy with the customer service over at 123-reg and will definitely be renewing with them as they were quick to act and very helpful.
Hopefully you should see speed improvements throughout the site and restored access, sorry for anyone who had speed or loading issues in the past.