I don’t know which one is it but you are either using private septic or city sewer. The sewer pipe between your home and whatever it is connected to appears to be clogged further away from your home than the plumbing rod can reach.
Once the plumber clears that section it is working fine until it fills up again with waste water and starts backing up into your plumbing fixtures.
If it’s not the sewer pipe problem it could be overflowing / malfunctioning septic tank (you’d need to find access to it), or some issue with the main sewer line at the street level (whatever you have). You’d need a plumber equipped with a video camera who can put it into the sewer pipe (after power rodding it) and determine what kind of an obstruction there is at 75’ depth or at wherever depth the rodding blade can reach.
If the main sewer line runs along or under the street there might be some access nearby and maybe it would be possible to get into that clogged sewer pipe from the other end.