I have a free mail account on this (german) website. If I type my password wrong I get, once successfully logged in, a message telling me about my failed log-in attempt.
Recently I noticed that from day to day the site notifies me of numerous failed log-in attempts (between 8 and 32). There is no feature as in GMail, where location and device of the failed log-in are recorded, so I am a bit in the dark. And also quite worried.
I have changed my password everday for four days now. Immediately closing the account is not an option since I still have to compile a list where this mail address is used.
What appropriate steps to secure my account are to be taken at this point?
The log-in attempts have declined over the last three days, maxing out at around ten altogether. Yesterday there was no failed log-in attempt logged. Nevertheless I resorted to your many suggestions and
- contacted GMX support, but have not heard back from them (certainly not using their 3€/min rip-off hotline)
- started using a password manager
- created easy-to-remember-but-hard-to-guess passwords
- started forwarding mails from the affected account to a more safe mail service
- learned about 2FA
- wrote down all the sites and services the affected address is used with, in order to swiftly be able to close my account
Since there are many good answers I will wait a few days and mark the one with the most up-votes as the final answer. Thanks for your help!