This can occur if the IsConstituent flag is set to zero in the constituent table. We usually only see this issue with converted records but it is possible to create faulty records via custom forms or batch templates which fail to set the flag.
The IsConstituent flag will need to be changed to 1 via a sql script.No other action should be required.
Steps to Duplicate1. Search for constituent
2. Constituent doesn't appear in the search list.