I am looking for a company who will not try to re-sell my domain when it expires. It is a very unpopular domain, no hit’s, no google rank, etc, but if I let it expire with godaddy someone will surely hold on to it for years. I contacted godaddy and they said to move it to another server...
I have a small webdesign business and one of my customers is crazy about someone using her name if she lets her website go...

I have a small webdesign business and one of my customers is crazy about someone using her name if she lets her website go...
You have to explain to her that, when she let her domain go, it COULD be picked up by people who closely monitor expired domains. It doesn't matter whether the registrar is listing it for sale or not.
The only way to make sure nobody else uses "her" name is to keep renewing it; it's only $10 a year, if she is so annoyed.

I am not sure i understand it correctly; if someone lets their domain get expired; they will not own it anymore and anyone else can buy it. If you are afraid you miss the payment (once a year) because they do not notify you correctly; you might search for a company which does not expire domain names but always will renew it unless you cancel their services. But nothing is going to stop them from selling the domain if you do not pay up.

It's simple, if your customer doesn't want to renew the domain then she will lose any right on the domain name, and that includes the ability to decide if someone like me or the average joe can register it.
If she is afraid of loosing the domain name if she forgets to renew it i'd recommend to renew it for several years.
For example i have all my domains with at least 2 years before expiration. Once a year i check all domains and renew all in a bunch, just one credit card charge to care about, just one invoice, quick, easy and only once a year ;-)

This is a two part 'problem'. Today domains typically won't 'expire'. GoDaddy will usually give you like a 20 or so day grace period to renew the domain. If you fail to renew it during that time period it goes into redemption period I believe.
Personally we cancel domains we aren't renewing and with GoDaddy they reclaim it under our name for a period of time, park it on their servers and see if anyone wants to buy it, also they take in ad revenue with the domains we cancel using our contact information the entire time.
In a perfect world and generally if you cancel a domain that's rather unpopular nobody is going to register it. There are still a few good names left:)

Personally we cancel domains we aren't renewing and with GoDaddy they reclaim it under our name for a period of time, park it on their servers and see if anyone wants to buy it, also they take in ad revenue with the domains we cancel using our contact information the entire time.
In a perfect world and generally if you cancel a domain that's rather unpopular nobody is going to register it. There are still a few good names left:)
In theory, registrars like GoDaddy are doing us a favour by offering a grace period, and together with the official RGP, registrants are guaranteed an extended time window to renew their expired domains. Of course, in the real world where there are greedy people and corporations, these domains are actually turned into parking revenues instead of being unresolved. The original owner's contact info is still on because he or she can still "reclaim" ownership.
More importantly, even without registrars sending expired domains to their own auctions or backordering services, there have ALWAYS been PROFESSIONAL "investors" closely monitoring expired domains on a daily basis. Don't even think you can slip one through under the table. Not a chance.

Yeah I agree, they are doing us a favor by allowing that "grace period" But they take that favor off the table if you don't renew and they go ahead park your domain on their dns servers, leave you as the registrant, and make money off it.

the 'grace period' is not a favour offered by registrars, is the registry who gives a 15 to 45 days grace period, and after that, another 30 days redemption period.
When the registrar gives a grace period and after that the domain is sold the customer loses the redemption period

the 'grace period' is not a favour offered by registrars, is the registry who gives a 15 to 45 days grace period, and after that, another 30 days redemption period.
When the registrar gives a grace period and after that the domain is sold the customer loses the redemption period
Pre-RGP "grace period" is a discretion of the REGISTRARS, who do NOT have to pass along that refund window at the registries to their end-users. That is why we have varying registrar-level grace periods, ranging from 0 - 45 days.
By the way, which registrars do NOT send expired domains to RPG?