There are at least two important issues here. First, a council must keep minutes in order for there to be a record of the decisions that have been made. Without such a record, any actions of the council can be challenged as unlawful. It follows that good record keeping is essential to the proper functioning of a council.
Second, much of the legislation that creates and defines parish councils refers to the "proper officer". A council cannot operate effectively unless it appoints at least one proper officer, with responsibility for dealing with council matters. Commonly, this is the clerk. It can be volunteer councillors, although they may not be paid by the council. In a larger authority, there is more than one proper officer, each with distinct responsibilities.
Anyone can take the minutes, so long as they are recorded, and approved by the council as an accurate record. But it is obviously desirable to have regular arrangements in place. The chairman or councillors can create an agenda, but a meeting without a published agenda cannot lawfully make any decisions.
In short, someone has to pick up the baton, whether paid or unpaid. Otherwise, the council risks its actions being unlawful, and in the last resort it becoming defunct. If you are concerned, it would be sensible to notify the legal officer of the district council so that they can keep watch on the situation.