The WiFi at my daughter's home was constantly dropping their 5 GHz connections. It didn't seem to be a problem with 2.4 GHz, but I checked both of their access points and found that 5 GHz had the channel width set at 80 MHz, which not all devices are happy with. I changed it to 40 MHz and there's been no issue since. I also noticed their 2.4 GHz was set at 20/40 MHz, and changing it to just 20 MHz has also cleared many of the connection issues they were having. They have two Roku players on the network (Stick 3600 and Roku 4) and both are working well with these settings.
Also, make sure the radios are broadcasting on supported channels. Roku devices only support the channels that are legal in North America, so for 2.4 GHz the channel must be between 1 and 11, and 5 GHz must be below 49 or above 148. Most routers/access points assign the channel automatically, which also means it could change without your knowledge. If it changes overnight to an unsupported channel, your Roku will no longer connect.