Member marked down even tough port is reachable

the monitor you note (the default https monitor) will quite likely produce a 404. You'd need to accept that:

in tmsh:

 
modify ltm monitor https yourmonitor {  recv "HTTP/1\.(0|1) (200|404)" }

If you wanted a completely new monitor (assuming you are using defaults), which you should use, in my opinion:

create ltm monitor https yourmonitor { cipherlist DEFAULT:+SHA:+3DES:+kEDH compatibility enabled defaults-from https destination *:* interval 5 recv "HTTP/1\.(0|1) (200|404)" send "GET / HTTP/1.0\r\n\r\n" time-until-up 0 timeout 16 }