1. I'm relieved that you and 46 other people (just the ones who clicked "I have this question too" have the same problem as I do. I thought I got a bad keyboard - Amazon is selling refurb's for under $30 (they actually look new, so who knows their provenance).
2. I used a Mac Mini for 5 years before switching back to Windows with an Intel NUC. I got the refurb keyboard for the NUC because it is compact and honestly after returning to the Apple keyboard I have to say the keyboard feel is SO much better than the Windows wireless keyboard I first used on the NUC. I miss the Delete key (forward delete, the one marked "delete" on the Apple keyboard is what win-worlders call "backspace" and I miss the media keys (work on MacOS but not on Win) but other than that the advantages outweigh the disadvantages.
3. This is the best Bluetooth keyboard I've ever used, whether on Mac, Windows, or iPad, or Windows tablet, or Android tablet. There is never ANY delay with keystrokes, and even in the morning on my Windows desktop I only have to hit a single key once to wake it from sleep, versus hitting several times for the Windows wireless keyboard to wake up.
4. The downside is that my first set of batteries only lasted 4-5 days. I am wondering if the instant, never delayed keystrokes, is a result of the desktop/keyboard "polling" each other to keep the keyboard awake. The biggest problem with most BT keyboards is that they go to sleep to fast and wake up to slow. On my Mac Mini, there was a slight hesitation for the first keystroke but none there after, at least not unless I went to lunch and came back. So I'm not sure whether the keyboard is defective - won't go to sleep - or if the Windows desktop is not letting the keyboard go to sleep. I'm glad this issue is hitting regular Mac users and not just on-the-fringe users like me, because it tells me my keyboard is likely not defective but instead the interaction between keyboard and computer is a little off - no sleep time to save the battery, is my best guess.
5. I'm going to try a different Apple Wireless Keyboard with the desktop computer and see how battery life is on that one. I will shift the questionable unit to iPad use, since iPad use is much more "structured" - everything off until my occasional cafe visit, iPad and keyboard on only during the visit then back in their satchel. Under that scenario, constant "on" is what I want out of the keyboard anyway, for sheer responsiveness. At my desktop, I DO want the keyboard to "sleep" after 5 minutes of inactivity. If, on the other hand, the different AWK works fine - for more than a week without killing its batteries - I'll get a replacement for the battery-eating one.
6. Let me sing the virtues of the AWK with an iPad. I was previously using an Amazon Basics Bluetooth keyboard - sized the same as the AWK but obviously not built to the same quality. Keys felt nice, but I had problems selecting text with the cursor. The cursor moved too slowly on the iPad 4 I was using, and something buffered keystrokes so it would keep selecting text long after I took my finger off the arrow key. With the AWK, the cursor moved a LITTLE faster but more importantly it wouldn't overshoot the text I was selecting, eliminating my big headache. Strange, huh? Apple is good in several ways: attention to details like this, and an enormous "pool" of hardware and users, with Apple tightly controlling both hardware and software, usually means when problems like this pop up, they get fixed sooner or later, generally pretty fast, compared to Win World where the varieties in hardware are insane.