First of all, you'll want to make sure you're actually seeing the most up-to-date information in the group. Go to the "Members" tab and click the "Refresh" button, that will populate the most current list of members. If you still don't see the constituent there, examine the type of group.
This behavior can happen if the group that you are adding the constituents to is dynamically populated. A good way to identify these groups is ones with a "Rebuild Group" option. If a group is built off of a query, anytime you manually add a person to that group they will only remain in the group until the group is rebuilt. Once the group rebuilds it will re-run the query, determine that constituent doesn't meet the criteria to be in that group, and kick them out. Some common types of groups where you'll see this behavior are:
  1. Interest groups
  2. Groups built using the query tool
  3. Groups built off of queries in Raiser's Edge
  4. Groups built from LCRM