It sucks but banks have always been that way. Are you with a small or large bank? I think the larger banks tend to have a number you can call most of the time. At least the ones in the US do. I don't know if changing your bank will really do much but I would definitely look at the options if there are issues.
This bank is relatively small in Finland, but has locations across europe. It is big enough though.
I am with another two banks for different things, so I will consider consolidating.