The attenuation might not change when they fix the box (that is mostly a function of distance to the DSLAM). If your phone is no longer noisy when it rains at least the physical issue has been fixed and you should no longer lose sync.
Time lags while surfing can be caused by slow DNS responses and/or the server for the site you want being busy. They are not necessarily related to a line fault. You can change the DNS servers you use...Google runs public ones at 18.104.22.168 and 22.214.171.124.
»code.google.com/speed/public-dns ··· ing.html