Messages not being sent, getting “spam” error

All of a sudden, my forms are not working anymore. They all get an error, and when inspecting the AJAX response, they are always marked with status “spam”. Here is the full response for one of my forms:

into: "#wpcf7-f222-o1",
message: "Failed to send your message. Please try later or contact the administrator by another method.",
status: "spam"

I used the wpcf7_spam filter to return always false (in effect disabling the spam checking), and it worked for a day. Now it’s not working again! What can I do? I have no idea what to do next, except remove the Contact form 7 plugin.