What percentage of professional pilots end their career early for medical reasons?
(US-based answer)

The problem with answering your question is that it isn't all clear what "losing a medical" actually means. If a pilot is denied a medical, the FAA will obviously know and you could probably get that data from them somehow, even if it takes an FOIA request. But what if you just decide not to renew because you know you'd fail? For all the FAA knows, you might have retired, changed career or even died.

If we assume you do mean "denied" then the only specific number I could (quickly) find for denials was from 1978:


  The annual denial rate based on airman applicants is 7.9 per 1,000
  airmen. By class of certificate applied for, the annual denial rate
  per 1,000 applicants is 4.5 for the first class, 6.0 for second
  class, and 10.2 for third class.


You could apply those rates to the number of airmen certified each year to get an estimate of the absolute numbers, but obviously using a 40 year-old report may not be accurate today. And determining how medicals 'map' to pilots may not be easy.

If you want a better answer, you'll have to define exactly what you're asking. To get an accurate number (whatever that means for your purposes) you might have to look for some specialized actuarial or medical research on this.