Annoying MMS problem
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.