How do I fix a wooden retaining wall?

Although it looks to be functional at this point eventually the bottom tier will rot away causing the retaining wall to fail. You have a legitimate concern. There is no simple answer to this because the right answer is to rebuild the wall. I'm assuming here that the wall has compacted soil on the other side. Since the bottom tier is rotting, and if you're willing to invest some sweat equity in this project, one less expensive option might be to cut out the bottom landscape log with a wedge and sledge or axe. This will be labor intensive but not expensive. Remove one section of the log at a time, removing soil by hand and shoring each section up with pavers/landscaping blocks of the same height as the log. Work along the entire length until you have replaced the entire log with landscaping blocks.

You will mostly have vertical pressure on the bottom log from the weight of the retaining logs above it and whatever structural material is above the logs. The bottom log will not have a lot of lateral pressure from the soil behind it. The main thing you need to do is make sure that as you remove small sections (a foot or two at a time) that the pavers you put in its place fit securely and are on a solid base so as you transfer the load to the pavers there is no compression of the course of pavers. If you do that you'll be fine.

Any soil under that bottom log should be well compacted but you could put a layer of pea gravel under the pavers before you insert them. If you tap them in with a hammer be sure to hold a wooden block over the side of the paver as you tap it in so you don't crack the paver.
The blocks don't have to be flush with the logs above. It will appear to be a base for the wall.