Check your handlebar grip clamps if they are pinching the wires you will short that fuse..
( ask me how I know this )..

 

My 2008 Bob does the exact same thing, I put in 25 fusses and ride it, like you I took it to HD and they found nothing. I have all spare fuse sopts filled up with extras and carry more on my case. I can go two or three weeks without blowing a fuse, then I will blow five in a day. I never use my turn signals anymore, hand signals only, if you come up with an answer let me know.

 

I am having same issue with a 2008 FLHX, to no avail to fix it. Help

 

another similar issue here...

 

Have you had a sissy bar fitted, this normally requires relocation of the rear turn indicators, or there could be a pinched wire under the new support bracket, My 02 worth,

 

Thats what it was on mine, HD never found it, had to figure it out myself

 

This is rediculus ... all these problems on new very expensive motorcycles. I love my Fat Bob but have had battery cable problems 3 times since i got it ... it's an 08 currently with less than 2500 miles on it. And I've read about others with bikes of the same year with the same problem. Is someone at the MOCO sleeping on the job? Geesh!