The module's name is WWW::Mechanize. Perl is picky about the capitalization of module names, so it's better to use a consistent, and preferrably the correct way of writing a module name.

The WWW::Mechanize documentation points out the autocheck parameter that you can give to the constructor if you promise to check the results of your calls to ->get etc. yourself.

The really generic way to do it would be to stick it in a loop and eval { } your get call.

In Perl, eval { } is what you use to catch exceptions. See eval.