I don't know about remember, but you might be able to fix the problem without rebooting. Did you try running ifdown eth0 followed by ifup eth0, or /etc/init.d/networking restart? The first two just bring down and up the network interface. The last one actually restarts all networked services.
Something that might help with the power cuts would be to purchase an Uninterruptable Power Supply (UPS). They're a bit pricey (~$40 US for a decent one), but I've paid for mine in the time it took to recover my system after one particularly bad power failure.