One of the frequent objections I hear about Problem Management is this: our Service Desk does not have the time.
I totally sympathise with this, having acted as both Helpdesk and Service Desk manager in my time. When you are under pressure it's easy to push something like this out to a permanent 'next week'.
The point is though that Problem Management is something that can help to reduce the number of Incidents you are dealing with - helping to take the pressure off... and the payback period can often be quite short. Serio supports Problem Management, helping you by keeping the Problems you log quite separate from Incidents.
If that doesn't convince you - try this: allocate a fixed number of hours each week to Problem Management by a member of your team (who you'll nominate as your Problem Manager). Do this for a couple of months, and at the end of that time see if you've got anything worthwhile from your investment.
I'll follow this post at the end of the week some suggestions as to how you can get started with Problem Management.