http to https irule

That makes more sense.

I would suggest adding logging to your HTTP to HTTPS iRule and see if your login request is being directed back to HTTP. If it is then it would make sense that your login attempts are failing.

when HTTP_REQUEST {
HTTP::redirect https://[getfield [HTTP::host] ":" 1][HTTP::uri]
log local0. "HTTP to HTTPS Redirect - Client [IP::client_addr]"  
}

What I am guessing your problem is:

Initial Access - HTTP to HTTPS Redirected

HTTPS Login Page - Login Attempt is made. Submit is sent to HTTP://www.website.com

HTTP to HTTPS Redirect - Login Attempt cancelled by redirect.

The logging should tell you if this is your problem.