Unfortunately, the printer adopted from the Bonjour protocol as soon as it goes into a non-defeatable power saving mode. Set the timer for one can not exceed 50 hours ago Ask (default is one minute), and then it's over with printing or scanning. The unit is still responding to a ping, and the configuration interface in the browser can also be addressed, but on mDNS inquiries it is no longer responding.
Thus, the device is not scanning even for printing from a computer accessible (just disappears as scan source, and print jobs hang), and also sets the AirPrint service.
Because a keystroke on the control panel does not wake the device, you have to the printer off and then on again, so that he again does its job. This is clearly a bug in the firmware, but the support of Brother speaks out and pushes it to Apple or the Bonjour protocol itself, which of course is nonsense, because other printers also do not have the problem.
I have the device shipped then in his crate back and replaced by the larger model DCP-L2540DN. This is indeed connected via LAN, but is likely in most cases (including my own) not be a problem, because a printer is usually not the middle of the living room, where a wireless connection is absolutely necessary.
So now everything works, and as a bonus you have now a real PostScript-compatible device (the L-2520DW is a GDI printer), which works a bit faster and of course also has a document feeder for the scanner. At first I thought, with my scan volume of perhaps a dozen or two pages a year would be a flat bed scanner is not so bad, but at the first trilateral document has vastly annoyed to have tigers between the computer and printer.
In this respect, the clear advice to grab for a few euros more for the same L-2540DN.