For example, to increase membership we need to increase activities, but to increase activities we need more members.
Mutually dependent: "Our physiology and that of the plants we eat are not only biochemically similar but interdependent" (Cindy Engel). - American Heritage Dictionary, 5th Ed.
Should you want a negative version, there is the IT term deadly embrace, where two pieces of computer code each wait for the other in an endless loop. It's not pretty.
This predicament is sometimes called a Catch-22. This phrase was used in the novel by Joseph Heller and was based on the difficulty of dealing with bureaucracy.
A common example is the Permissions Paradox. This is the predicament of being unable to get a job because you do not have experience, and being unable to get experience because you do not have a job.
A more informal reference is the Hole in my Bucket syndrome, based on the humorous song in which it is impossible to repair a bucket without water, and impossible to fetch water without a bucket.