Sometimes, my harmonica will be out of tune, and I won’t be able to make a sound, no matter how hard I blow.
Then, it’ll go back to sounding fine.
Is there something wrong with my harmonica?
Mine sounds bad when I try to play it.
Try Sucking. 
I got nuthin’. Happy T-day.
Maybe you have gunk on the reeds that eventually falls off? Hard to say but a bit of googling brings a couple of sites you may want to look at:
I opened it up, and couldn’t find any dirt or any problems with the reeds.
Could it just be dirty from saliva, since I haven’t cleaned it since I got it?
What make and model is it? Some are just junk.
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Moving thread from IMHO to Cafe Society.
Are the covers dented at all? It could be the reeds are binding on the plates. If it’s given up the ghost, they’re not to expensive to replace generally, especially the diatonics. I’m partial to Hohners like the Marine Band, Hot Metal or Blues, personally.
It’s a Hohner Special 20.
Those are good quality, so I don’t know what to tell you.
Normal wear and tear will cause all harmonicas to eventually go out of tune. Sometimes the reeds can be “retuned,” but if they’ve cracked or worn too far they will need to be replaced.
Honestly curious, what’s a new harmonica cost these days?
Depends on the key, among other things. If it’s a common key like C, you can often get one more cheaply, like ten bucks. More unusual keys (and there are 12 altogether) may cost more because they are more specialized, like 30 bucks each.
A Hohner Special 20 costs under $40. A Hohner Blues Band cost $7. Of course, the German-made Special 20 is pretty much guaranteed to work well; while the Blues Bands can be hit or miss.
A Hohner Special 20 should be fine. Are you having this problem only with some reeds or all the reeds? If it’s a particular reed, it could just be gapped a bit too close and you’d need to bend it a little more open ever-so-slightly. Typically, though, I find harmonicas out of the box gapped a little bit more loose than I like them.
You shouldn’t need a lot of air pressure to make a reed sound. The problem can also be your sounding technique (I was about to write “blowing technique,” but that didn’t sound right.) If you direct the air at a weird angle, it can cause the reed not to sound.
Also, yes, saliva can gunk things up a bit while playing. I like to give the harmonica a few solid thwacks against the heel of my hand or side of leg or whatever after playing a bit to get any excess saliva out. When I was starting out, I seemed to have this happen a lot and after awhile, I managed not to need to shake up the harmonica as often. Playing louder/more aggressively tends to do that, at least with me.
I’m guessing the last is the most likely culprit, especially if it’s bouncing back into normal playing conditions and not remaining difficult to play and out of tune.