Good question Dobby! This is something that would be really helpful since as you probably know, we can’t get into space to fix our satellites (they did once send satellites into space to fix the hubble telescope which was the first and only time a satellite has been fixed in space!). In a way we try to design our satellites to be able to get out of trouble. For example if something fails, say one of the reaction wheels which helps keep the satellite steady, there is an inbuilt sequence of commands in the software which makes sure the satellite gets put into a safe mode until someone on the ground can investigate. We also make sure we can upload software from the ground to space so if we discover something wrong we can try to fix it with software.
There are some interesting mission ideas to use tiny little satellites to build bigger ones, like lego! This could mean that if one of the blocks fails another one could take its place. Cool!