RN102 ReadyNAS problem accessing files

The IP address can be assigned one of two ways: automatically by your router via DHCP (which is the default), or statically, within the NAS (or other device) itself.  Your router will typically reserve a DHCP address for a device for some time even when it's not on the network.  So, short power-offs don't normally result in a re-assignment of the DHCP.  But long periods can.  Changing the router most certainly will.  Another thing that can cause a re-assignment is if some other device "grabs" the original, but I doubt that's your issue.

Many get around the possibility of a "roaming" address by using a static address assigned in the NAS.  But I don't recommend that.  If you do so, and then swap the router for one that uses a different address range, you'll also lose access.  Instead, go into the advanced options of your router and permanantly reserve an address for your NAS.  How you do that varies by brand.  If you do swap out your router some time later, the address reservation won't follow, but you can use RAIDar to locate the new IP address and/or go into the new router and re-assign the IP address you desire.  If you do go into the router settings and change the address assigned to your NAS, you should re-boot the NAS to make it "take".  If you just make the currently assigned one permanent, it's not necessary.

Using names instead of IP addresses is also supposed to get around this, but I find the Windows isn't especially reliable in properly accessing by name.

While not applicable to your 102, I do want to add that the IP address is assigned to the hardware MAC address, so is different for each port on a NAS with two Ethernet connections.  So a changing address can be due to inadvertently swapping ports.  Someone with another NAS model looking for a solution for a similar problem may find this useful.