Many thanks for this workaround. I have recently purchased a Brother HL-3140CW, and it is very hit and miss as to whether I receive the "No airplay printer found" message. Sometimes I will find the printer no problem, other times I will not. The printer is in "Deep sleep" mode.
Your workaround definitely does the job, but it's obviously extremely frustrating to have the problem in the first place. It also adds an extra step to what should be a very simple process for my (non tech savvy) parents to learn.
I have experienced the problem on an iPhone 5S (iOS 7.1) and an iPad mini (also 7.1). I am unable to test on an Android device, so personally I'm unable to point the finger squarely at Apple as in the case of js2345.
I do have an old iPhone 3GS, which is running iOS 6.1.6. However, I'm not sure this is much use for testing, as even when my 5S is connecting to the printer OK (i.e. I do NOT receive the "No airplay printer found" message), the iPhone 3GS cannot connect. I find this strange, since lemon-kun mentioned above being able to successfully connect with an iPad running an older version of iOS... 5.1.1 compared to my 6.1.6. Is it device specific rather than OS specific as to whether airplay devices can be connected to?