Hi there. Last week, our septic tank backed up and we had a to have a plumber come out and clear the line for us. A similar thing happened last year, and we actually had the septic tank drained as well, so I know the tank isn't full. Upon cleaning the plug this time, the plumber noticed that the cap to the sewer had been broken and he urged us to get a new one asap. I did buy one, but didn't put it on yet, and now the sewer is backed up again. I wasn't sure if not having a seal on the septic system could cause things to back up or not. I am going to put the cap on today, but I am hoping I don't need to call a plumber again and spend another $250 on it and that once the cap is back on, things will flush/drain normal again.

A missing clean out plug will not cause a back up. That is unless somebody or something is putting something down it.

If snaking the line cleared the line you had something blocking it. What kind of snake did the plumber use? If he used a drain snake, which would be about 1/2 to 5/8" diameter, he probably went through the blockage but did not clear it. There are three types of heads on a drain snake. First looks like a big spring with a hook on then end. The second is a spear point head and third is a cutter head. A plumber would start with the spring type. If the water started to flow he would assume he had cleared the blockage. However the blockage might be something that closes up later and stops the flow again.
That is most likely what has happened.

The other type of snake is a sewer snake, much bigger, about two inches in diameter with a big head that clears the entire pipe. Much more difficult to use. Can be dangerous to use.

You can rent a drain snake and clear the blockage yourself. Wouldn't recommend you try to use a sewer snake.

Just for your information a septic tank is always full. A septic tank is simply a holding tank. It provides time for the solids to dissolve. There are always some things that don't dissolve. These things settle to the bottom of the tank. The sewage comes from the house and enters the tank just below the top. As the sewage builds up it flows out the distribution lines which are just below the sewage input lines. Therefore, the tank is always full.
However if the solids in the bottom of the tank build up they can float up and go out the distribution line, clogging the lines and the surrounding gravel and soil.
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You don't pump a septic tank to empty it, you pump it to remove the undissolved solids.

Also if you have had an excessive amount of rain the soil may be so saturated with water that it can not absorb any more moisture.

In either case the tank may be so full that it cannot take any more liquids.

Tree roots play havoc on sewer and distribution lines.

Suggest that you rent a drain snake and snake the line again and see what happens. If the problem continues you may have to consider replacing the distribution lines or at least adding an additional distribution line.