No. Once properly installed, the chip will not migrate or move.  It will be there when you need it.  (A study published in the Journal of the American Veterinary Medical Association (2003 223:1316-1319) revealed that microchips properly implanted in the nuchal ligament do not migrate.)

Here are some technical details on the EquineChip:
• Bio Compatible Glass | Made by Schott®
• Anti Migration Coating | Smooth Parylene® coating on all of our chips.
• Needles | Stainless steel, extra sharp 15 gauge ‘mini’ needle.
• Warranty | Lifetime Warranty on Microchips.
• EtO Sterilization Process | Unopened pouch guaranteed sterile for 5 years.
• Recyclable Materials | Packaging, plastics, paper and needles.