Suggested messages with the type, "Solicitation" will be hidden if the TeamRaiser status is not set to accept gift. For example, if it's set to "Accepting Registrations Only", these suggested messages will be hidden from the Participant Center.

Resolve this by following these steps:
Edit the desired TeamRaiser
Go to the last page of configurations called, "Publish"
Under "1. Status", select a status that includes Gifts.