Actually, each time you push a pin link out it weakens it structurally. The chain pin has small flanges on the ends to hold it in place better. When you press it through the link with a chain tool you bend these flanges a little bit. The chain pins really aren't designed to be pushed laterally and maintain strength. This is why Shimano makes their special replacement pins and SRAM makes the quick links. Like you, I have used non-replacement pins in a pinch and they definately got the job done. Most of the time they would even last me mulitple rides. Eventually, the chain would break at that same link though.
Do yourself a favor and buy some quick links or powerlinks for your chain in an emergency. They are WAY easier to use too. The SRAM link for an 8 speed chain will fit Shimano chains that are also 8 speed. I am not sure if the same is true for 9 speeds though. I am sure you can find more info on this site about it.
If you stay with a regular Shimano chain and don't go the quick link route, there are some simple procedures that will help you put less stress on the chain and hopefully allow it to last longer. Try to make sure, when you disconnect a chain, that you disconnect the chain at the proper pin and link. A full link consists of an outer (wider) link connected to an inner (thinner) link by a connecting pin. You want to pull out a FULL link (inner and outer) when replacing. (See the tech doc below. A visual is MUCH easier to understand.) They SAY this is the "preferred" method of link removal because it makes for a stronger chain.
Lastly, if you are having stiff links after replacing chain links, yuo can easily loosen them by simply putting a little lateral stress on that specific link. The easiest way to do it is to grab the chain like you would if you were going to snap a pencil in your hands. Put your thumbs on either end of the link that you want to loosen where the pins get inserted and push and pull against the pins laterally. It may take a little bit of pressure so don't be afraid. This will eventually loosen that link up enough that it will freely bend like the others.
Hope this helps and I didn't bore you to death. Good riding.