I do not see the SX435 listed on Apple's list of AirPrint compatible printers <iOS: AirPrint 101>. Are you sure it is not a TX435 or SX535?
I consider it deceptive when a printer company claims a model will work with an iPad, and doesn't make it clear that you have to have their custom App. If that is the case, you need to search the App store for the Epson App. You may not find it very useful, but it should get you printing.
In case your printer really is AirPrint compatible, your WiFi router may not correctly handle Bonjour data required by AirPrint to find the printer. You would need to contact the router's manufacturer to see if there is a change in its setup or a firmware update that will solve your problem.