I have a cisco2811 with a 64MB flash card, I bought a new 256MB.
Can I remore the flash card when the router is up and running without it crash?
unless you are running applications like CUCME ( call manager express) you can do it because IOS image is loaded and expanded in system RAM at boot time.
There can be other cases where on flash are saved useful files like vlan database if your router has an etherswitch module.
However, you probably need to upload with TFTP or FTP the current files in flash: in order later to write them on the new bigger flash
I also recommend you to format the new flash on the router before writing files over it.
Hope to help