Mark,
You can generally assume that you are going to pay a serviceman roughly twice what it would cost you to replace a timer yourself. The pro has a right to a legitimate profit if you hire him; you have a right to save money if you are reasonably handy.
Replacing the timer in just about any home appliance is rather trivial. But you have to be good at diagnosing your problem because you aren't likely to find a parts dealer who will let you return an electrical part. This is very reasonable, because too many amateurs are capable of ruining the new electrical part and attempting to return it as "defective."
The manufacturers build most timers in a manner which make them rather difficult to work on. Still, many timers can be repaired by a good DIY homeowner. I've had extremely good luck with dryer times, about 50% luck with washing machine timers and very poor luck repairing dishwasher timers. Even if you aren't brave enough to try fixing one, I'd recommend tearing apart any timer that you have replaced so that you can determine how complex it is, whether you can locate its problems, and whether you could repair & reassemble it. It develops self-sufficiency skills - which may be very important if the timer that you need is no longer manufactured.
If I determine that the timer is the problem with an appliance, then I'm going to remove the timer. If I'm too busy to mess with attempting to fix the timer, then I take it to the parts dealer along with a serial number and model number from the appliance. If I've got the time to try fixing the old timer, then I've already removed it and I can do my experimenting on the old timer before making that trip to the parts dealer. Nothing is lost except for a half hour or so of tinkering. Sometimes the fix is nothing more than using an emery board and then sandpaper to restore a set of burnt contacts.
I strongly recommend working on your own appliances if at all possible. Your lifetime savings will be considerable. Plus you will feel less vulnerable when you do call in a pro and he recommends expensive repairs.
To make your timers last longer: Periodically warn everybody in the house that you will break their fingers if you catch them turning an appliance timer knob counter-clockwise.
Gideon