The error message displayed (“An error occurred while processing your request!”) does not appear to be within the plugin. So it is likely one of two possibilities.
If you have customized any of the plugin’s dialogs that are translated, note that you can’t do that in a multi-language situation. This is because the original string is needed to find the appropriate translated string. If you change the original message, that string will not exist in the translation file so no translation will occur.
The other possibility is that you have another plugin or custom process hooked to a WP action that is also used by WP-Members during registration and that is triggering a message from that plugin/process. This seems like a likely scenario since you mentioned this started more randomly, then went away, and came back. If you installed a plugin to test, turned it off, then turned it on again, that may be your culprit. I would look at other plugins you may have installed recently and test without them to see if that may it. (Alternatively, a quick way to review it would be use a search/replace tool like grep on your filesystem to find that exact message string to see what file it may exist in.)