The first thing to try is to identify if there is a compatibility or IP range issue with the network or if it is the device itself.
Take the device to a friends house (who preferably has a different brand of router) or a public Wifi at a coffee shop and use it for a while. If it drops while on other Wifi networks, it is not you it is the device. Otherwise, if it works fine there, it could be a strange compatibility issue between the device's WiFi chipset and your WiFi's chipset, (rare) or an issue where more than one device is trying to use the same IP address etc.