Here's my

(what my advice is generally worth):
If you charge a fee you are working as a professional, meaning the
customer now feels there is an implied level of performance. Failing
to meet their expectations (ie: not finding the ring) will leave them
with a bad impression of detectorists. Every time they see a metal
detector they'll remember the guy who took their money and came
up empty handed. On the upside... if ya find it you're a hero, and
you made a few bucks as well.
The way I see it I'm doing something I enjoy doing, and making new
friends and gaining new permissions as a result. Even if you don't
find their lost ring, they will know you did your best and you leave
them with a positive impression of detectorists.
Those who consider themselves professionals and find lost items
for a living are perfectly justified to charge a fee. I believe hobbyists
(like most of us) are better off creating good will and, as suggested,
gaining new permissions for sites we might otherwise never have
a crack at.