My experience with this type of problem has to do with soap buildup from a dishwasher in the pipes near where it enters the main sewer pipe. For some reason the soapy stuff builds up a little and then the stopped up water dumps some more etc, until the whole thing is plugged. Similar to a bird building a nest.
You can try some drain cleaner, but what it will probably take is a snake or a running garden hose to break the stuff loose and force it out. I know it is unconventional, but I have had more success with a 50' garden hose than with a snake. I put a plug in the sink drain (or cap it) and then run the hose (running) in through the cleanout if there is one or through the roof vent. Eventually you will reach a point where the hose will not move any more - just keep jabbing at the obstruction until it breaks loose. Once it breaks loose, all of the water in the pipe will flush it quickly into the septic tank and you are good to go for another year or so.
If the pipe has a dip in it, the same kind of thing can happen. I had that happen on a 3" pvc run above my tuck-under garage in the floor under the kitchen. There were not enough support hangers to hold it straight. When the 3" pipe plugged up, I was amazed - I had to cut it out to clean it and replumbed it with a cleanout. But after I installed more hangers, it no longer had a problem.
