An adopter or purchaser who signs an agreement under section 54-638 shall cause the adopted or purchased dog or cat to be spayed or neutered on or before the date stated in the agreement. If such date falls on a Saturday, Sunday, or legal holiday, the date may be extended to the first business day following such date. The releasing entity may extend the date for thirty days upon presentation of a letter or telephone report from a licensed veterinarian, stating that the life or health of the adopted or purchased dog or cat would be jeopardized by spaying or neutering, and such extensions may continue to be granted until such veterinarian determines that spaying or neutering would no longer jeopardize the life or health of the adopted or purchased dog or cat.