That is actually a very good question. And the reason I say that is because i have had to deal with the aftermath of someone's "Computer Guy" repair that went wrong. just to find out that their "Computer Guy" is the neighbors 15 year old who "knows" computers. I have been working as a computer tech for over 15 years... wow, has it really been that long... anyway, i have worked for retail stores, independent repair shops and currently for a major university in Central florida. all those jobs i was a tech. not a manager, receptionist, etc. i was a computer tech. i have done repair for your average home user as well as large companies like the United Way, University of Miami (they didn't have a printer repair tech), etc. and at my current job i have repaired everything from student computers to the president of the school. (talk about someone who holds your fate in their hands).
Yes, it has to do with cookies, but more than that it has to do with how they are programed. some sites to make themeselves more secure are written with fail safe system that 1- will not allow your to save your password (there is a way around that i will get to it later, works SOME of the time) or 2- will only save it for a short period of time. since i am not sure what sites you are refering too this is an educated guess but i will give you an example. eBay will keep you logged in for a day. after that you have to enter you user name and password again. my bank requires that i enter both user name and password. it will not save it on my system. but there is still a cookie on my system that identifies it as being me. if the cookie is missing i am asked a third question to make sure that i am the correct user.
a way around the password issue is to use a different web browser. web browser is the program you use to see webpages. Firefox does a much better job and storing passwords. the reason it can get around some of the security is that a browser is basically a translator (not exactly but its close enough as an analogy) that takes the code that is written and turns it into a page with pictures, animation, etc. Since Internet Explorer comes built in with every windows machine, it is the most popular. so when they write the code, they write it for Internet Explorer. since Firefox "translates" the information is a slightly different way, it is able to do things that I.E. can't do. but it can also cause sites to look a little different. the fonts (style of the letters used) can be different as well as their size.
you can't really do much about how a site is written. other than try a different browser. (you can download firefox for free at
www.download.com )
by the way, i am or have been certified tech for Apple, Dell, Hp, Compaq, Toshiba, IBM, eMachines, Gateway and some brands that don't even exist anymore. some of the certifications are only valid if you work for an authorised repair center. where i currently work is not HP/Compaq certified, my certification is not valid. however if i was to switch jobs for a place that was certified, then i would be back in business.
Sorry for being so detailed but i rather give too much information than not enough.