How is de-synchronisation of HOTP solved?
The usual resynchronization method involves getting several consecutive codes from the token and then running the algorithm once with a very large look-ahead window until the set of consecutive codes are found. The number of consecutive codes needed depends on how far off the token is.

With a typical token, two codes would suffice to handle a desynch of 200. Many HOTP systems will simply ask you for a second code and fix a desynch of less than 500 codes or so by themselves.