Hi Charlie, I had this same issue and my problem turned out to be that ModSecurity on my server was blocking invisible recaptcha from running. I checked my apache error log and found this:
[Mon Dec 04 19:02:07.978574 2017] [:error] [pid 56172:tid 140038914397952] [client 10.20.7.250:45296] [client 10.20.7.250] ModSecurity: Access denied with code 402 (phase 2). Operator EQ matched 0 at ARGS. [file “/etc/apache2/conf.d/modsec2.liquidweb.conf”] [line “532”] [id “5000214”] [hostname “usswichita.org”] [uri “/wp-login.php”] [unique_id “WiXh-3w54hqHYWVt9ZQVagAAAE0”], referer: https://usswichita.org/wp-login.php
I contacted my web host and they whitelisted the modsecurity ID 5000214. Once they did that then my forms and wordpress login worked perfectly.
I hope this helps!