Is there an expiration period to a verbal agreement to sell shares to someone else if the transfer hasn't happened?

It is possible that the contract to which you refer could be considered one for the sale of securities, which is a type which may need to be in writing to be enforceable.  Assuming that the oral agreement is binding, however, if there is no time specifiied for payment, the law will imply a reasonable period, which can vary depending on the type of contract and other factors.  If payment is not made within that time period, the buyer has breached a material term of the contract and you are excused from performing.  Having entered into a binding contract to sell your shares, your current desire to sell or not is irrelevant, as is the changed value of the shares (except to the extent that it is evidence of what a reasonable time period for payment would be.)