Why do spoke nipples keep falling out? I have a road bike with road tires. I commute on a paved trail that is fairly bumpy through a couple places due to roots pushing the asphalt up.  

My problem is that about once every week or two, I have a poke nipple completely loosen and fall inside the wheel.  I've had them replaced with brass nipples, but even those will fall out.  

Is the bumpiness the cause of this?  Should I expect the wheel hold up to this seemingly normal amount of wear and tear?  Should I ditch the wheel and buy a new one?  What's my best and hopefully most economical choice here?
This is a strange problem you're describing. Having them chronically come loose to the point of falling off is not a common problem, and even so the obvious solution is more/proper tension, but if the wheel was essentially rebuilt already (all new nipples?) then one would hope it's in the reasonable ballpark, 100-120kgf drive side depending on the parts used. If you only mean to say you've had the lost ones replaced with brass, then getting the whole wheel tensioned up would hopefully fix it. 

The other thing to do is apply a no-disassembly-required spoke prep such as DT Spoke Freeze or a wicking oil-resistant low/medium-strength threadlocker such as those made by Loctite or ND Industries. A small drop is applied at the spoke/nipple interface on each nipple, and it wicks in. It only takes a minute to do the whole wheel so it's a cheap solution if it works. Many but not all bike shops have this in the shop.