You can extend the life of a router significantly by being willing to fix them.
I recommend getting a good soldering iron and an additional cheap desoldering iron (the ones with the little bump attached to them)
After that, check to see if your multimeter can also act as an ESR meter (many will do both)
When the item refuses to start or work, desolder the capacitors and test them to make sure they are still good (not all caps bulge when they fail)
If you lack the proper testing equipment, then there is another thing you can do, (for small capacitors, you can heat the cap it's self up then bend them, this will cause the pins cap to come out, leaving the pins in place, you can then take a replacement cap, then hold it in place and see if the item boots. This method works if you are only dealing with 1 or 2 suspected bad caps.
(PS for devices with ample space for higher components, if you notice a poor design, eg a capacitor almost touching a heatsink, then you can solder on a female pin connector, then simply trim the leads to the same length on the replacement capacitors, then stick them in, this makes replacement easy when the cap fails (if the item will be moving, then add a little bit of hot glue to better secure it)
Most router failures are linked to passive components failing, (eg a bad diode, bad capacitor, or failed resistor)
PS if you know the nominal power usage of the router, you can run it inline with a multimeter to measure the power draw, then when it fails, compare the numbers, if you see a spike, then check the power rail and see if the resistance is just too low (indicating a short). If you get a short, then track it down and hope it is just a bad component and not short of a copper layer within a multi layer PCB, as those are difficult to fix, even if you can drill out the short without cutting any important thin traces, the loss of material in one of the layers can impact the integrity of the data and lead to an unstable device, even if it boots.
Edit: wanted to also add that some routers will overheat, eg I have tested a few from linksys and netgear, and it was not uncommon to see the thermal probe on my multimeter, reading 80+c with a ambient temperature of around 75f
If you want to keep temperatures under control, I highly recommend adding a heatsink once the router is out of warranty. you can buy cheap chipset heatsinks from sites like ebay, or salvage them from old broken computers. You can then attach them using thermal tape.
