Here is a link to previous similar question which might help -
https://answers.angieslist.com/I-repa...
If a commercial booster or lift-type recliner, I would check manufacturer website for local service reps - if no help there, contact local furniture stores carrying that brands about whether they do repairs or can refer someone who does.
If a medical chair, then contact local vendors in the Home Healthcare - Medical Equipment and Services providers category in the Health area of Search the List - have the make and model info at hand when calling.
If disability is service-connected or aggravated and this is medically necessary equipment to meet ADL mobility requirements, the VA or Medicare/Medicaid (if so covered) or your insurance provider might cover the repair or a new chair - contact your medical provider if medically necessary device like an electric booster chair (electrically boosts you up and down to/from standing position).
Otherwise, Furniture - Repair and Refinishing would be the normal Search the List category for this type of repair. If no such luck, contact local furniture stores that sell recliners and ask if they know anyone in town who repairs them - most stores do not do repairs like this themselves, but will know if there is a local repair guy.