I am having an annoying problem on my Galaxy Note 3. For whatever reason, MMS will not send/receive on my WiFi network, but as soon as I turn off WiFi and connect to my carrier's network (T-Mobile) it works. It used to work on WiFi just fine, and we did not make any changes to our network when this started. I have had this phone for about a year and 3 months (it is preowned). Any suggestions? I have rooted this phone (Kingo), but the problems started before I rooted.
MMS service is a carrier service and is sent over a cellular network (see: wikipedia page) so you need to be connected to your carrier and it does not work solely on WiFi.
It is quite normal that you cannot send it over WiFi but as soon as you connect to your carrier's network, it works.
I suspect that in your previous experience, you may have been connected to both your WiFi and your carrier, used WiFi for Internet connection and used MMS over your carrier without being aware. If you later started turning off your carrier connection when you are connected to WiFi, this issue may have surfaced.