The person who keeps inviting you gently is leaving a path back without demanding a reason for leaving.

Some people hold a door open without asking why you walked out of it. When someone has withdrawn, from a group, a friendship or ordinary social life, the usual response is to want an explanation first, which makes returning a matter of confession. A steady, undemanding invitation removes that toll and lets the person come back when they can rather than when they can explain. Very often there is no tidy reason to give, only a difficult stretch.

If someone has gone quiet, keep including them without requiring an account of the silence. If you are the one who withdrew, you are allowed to reappear without a speech.