Fantini, I agree that you don't want to continue burning up starters. Replacing the starter relay with a Honda OEM unit may be your answer, but let's do this simple test first which will give you an answer with no guesswork. This test will determine whether your problem lies with your wiring, or with the starter relay itself.
Before starting the test, remove the large starter wire from the starter relay. This will keep the starter motor from running during the test. Leave the battery wire on the relay as normal.
1. Attach your volt meter to the starter wire terminal on the starter relay (the terminal that you just removed the starter wire from).
2. Turn the key on and push the start button. You should read 12 volts on your meter.
3. Now release the start button and turn the key off. According to your original post, I expect that you will still read 12 volts now (even though a healthy system would read 0 volts).
4. Keep the volt meter in place and open the connector for the two small wires on your starter relay. When you open this connector, if the volt meter goes to zero, then the problem is with the wiring in your machine and further testing will be required to find the problem. If the volt meter continues to read 12 volts after opening the connector, then the problem is due to internal sticking of the starter relay, and the starter relay will need to be replaced.
You might have to repeat this test a few times to get a reliable answer, because if the problem is due to internal sticking of the starter relay, it may not stick every time.
-Ken