It can happen on any phone. New or Old, depending on the phone's specs and also on your connection. If through WiFi, it is less likely the connection, unless the WiFi has issues (or to many devices on it).
Now if it is through data, then it would not be surprising. Most carriers/service providers have it so that your data speed will lower after a certain point. Either when you go past the limit the account has for data (for carrier/service provider where the data isn't just turned off after that) or if they feel you are using to much data. You would have to ask the carrier/service provider about that one.