A fuse blows because the current through it exceeds the maximum rating. That almost certainly indicates an electrical problem, most likely a short-circuit, in the appliance.

Replacing the plug doesn't fix the problem. It will be likely to simply blow again. If it doesn't that probably just means that the dri buddy has an intermittent problem - like a loose bit of bare wire which occasionally contacts something it shouldn't.

If you're not qualified to investigate and fix it yourself, you could look to find someone who is - there are some local organisations around the country (called things like "repair cafe") where suitably skilled volunteers will help, otherwise you'll need a professional at which point replacement may be more cost effective.