Here are some suggestions from a non-mechanic type person. First, make sure you are using the correct fuse. If it isnt the correct one, you are likely to be burning it out because of the load of current.
If this is not the case, the fuse is likely to be burning out because there is something causing a short in the circuit. My suggestion is to open up the rear light and to look for a cause for the short circuit (if there is one). It may be easier to remove the whole lamp as there are only a few bolts and you can easily remove with the tools provided in your tool kit.
With the rear light the contact point is a metal plate that extends to the whole rear lamp which includes all the bulbs. Make sure that the plate is not compromised as a result of corrosion etc. Also look for any loose wires. Hope this helps.