I googled my problem and found this thread... it's very similar.
I have a 2011 iMac, a late 2014 MacBook Pro Retina, an iPad mini 3, and iPhone 5c. Every device is running the most recent OS update. My iMac does not support handoff but it does support text and call forwarding... it's one year too old for handoff. But my MacBook Pro and all my iOS devices do support handoff.
Almost ALWAYS handoff works perfectly going from Mac to iOS, but the other way around was not always working. So I started playing with a few different scenarios and that's when I noticed it.... the screen of my iOS device has to be on and the app I want to handoff has to be the foreground app. Like, if I have a text message open on my phone, the handoff icon appears on my MBP, but the second I turn off my iPhone screen (I even keep the app open) the handoff icon disappears from my dock. Turn the screen back on and unlock the iPhone, and bam, it's back.
Now, I don't know if this is the way this feature is supposed to work or not. I also haven't found any obvious way to mess with the settings for handoff, but I really haven't looked very hard... or at all. However, and this may just be me, but wouldn't it make more sense to allow handoff from an iOS device with the screen off? I mean, if I'm in my car and I get an email, and I open that email and start reading it while I'm walking from my car into my office, before I sit down at my desk my natural instinct is going to be to turn my iPhone's screen off and put it in my pocket. Then I open my MacBook Pro and log in... wouldn't it be nice for the handoff from that email to be sitting there in my dock waiting for me? It doesn't make sense that I should have to pull my iPhone back out of my pocket and unlock it just to invoke that handoff icon. In my opinion it defeats the entire purpose of handoff because I'm back to using two devices at the same time, only to invoke the handoff dock icon. The process of pulling my phone out of my pocket and unlocking it does not take any less time than opening the Mail or Messages app directly from the Mac and finding the message I was looking at, especially with how my phone gets stuck in my pocket sometimes.
I don't know if its common knowledge or not that you need to have your iOS device screen turned on and the app in question in the foreground in order to handoff from iOS to Mac, but in reading through this thread I didn't see it mentioned. So maybe I helped someone realize more about how the feature works... maybe I didn't.