Plumbing mystery

So I have an odd issue with the plumbing in my house. In one of the bathrooms, the toilet occasionally doesn’t flush. If you try to use a plunger, the toilet doesn’t drain, but you can hear gurgling in the 2 sinks and the shower in that bathroom, and this gurgling comes with a smell of raw sewage. There is another bathroom on the same side of the house which works just fine, and the pipes from the affected bathroom use the same line as the unaffected bathroom. No other drains or fixtures are affected.

Here is where it gets odd:
– It happens frequently, almost always in the spring and fall
– It has been happening for the past 4 years
– The toilet will remain clogged for a day or two, and then it spontaneously begins working again
– Once when it was clogged, I opened the front door to leave for work, and my wife yelled and told me that opening the door fixed the clog
– We had a plumber come out. Of course, by the time he got here, it was working. They put a camera through the pipes, charged us $500 for the hour he was here, and told us there was nothing wrong. Three days later, the toilet stopped working again.

The wife gets pretty aggravated. So do I. Any suggestions?