I'm not sure if there is a "great" way to manage it.
At our church, we only put a page in the bulletin with the prayer requests of "immediate family" of the church.
All other requests are sent out to an e-mail group called "Mountain Movers Prayer Support".
People sign up for it and then they get regular e-mails.
We also have an internal e-mail list for staff to know what special prayer requests there might be.
If it were me, I'd make an announcement that the prayer list needs updated, and if you want to keep someone's name on the list, to please contact you.
Otherwise, the request will be dropped after 2 weeks.
This is to keep the list current.
One way I did our list was to divide the requests into different groups, like Unsaved, Illness/Surgery/Recovery, Wisdom and Direction, and Praise.
The biggest issue I had was the chronically sick who were not ever going to get well, whose names were on the list forever and ever with no real update.
I finally just listed some general categories, like Chronically Sick or Terminally Ill, Missionaries, Unspoken, etc.
That shortened the list a lot.
Yes, we need to pray for the sick, but for those who have a chronic bad back or diabetes, we can better pray when there's a flare up or surgery, rather than leaving the name on the list for years and years.
After a while, people start ignoring those names.
You might get a few disgruntled folks over it, but I wouldn't sweat it.
When someone died, I would remove their name from the list and add a request for the family under the "recently bereaved" for a few weeks, then remove it.
I also put an area on the list for "This week's new requests" and bolded the area for Praises.
Ahhh - gotcha!
Well, we have notes as to who put in the request and it runs one week.
If needed, an update is put into the bulletin (week 1 - Pray for Bill as he is having surgery on his knee.
week 2 - Praise that Bill's knee surgery went well.
Pray for his recovery.
week 3 - ___________ (no more listing unless Bill needs continued prayer).
Our secretary is great with this.
Additionally, the pastors are usually up to date on the members and their family as to what is going on so they will update when needed.
If they don't have the info, the secretary gets on the phone and asks if there is an update.
But we have things falling off the prayer list regularly - each week looks almost completely different.