Yes they run out at DLR, but they also run out at WDW.
Here is what happens at Space Mtn (similar at WDW but some different details):
Let's say you go on a day when DL opens at 8AM. Those who get the first SM FastPasses (FPs) will have a return window of 8:45-9:45AM. There will always be at least a 45 minute delay until the return window. As more and more people get SM FPs, the window gets pushed out. On a busy summer day some time around 9AM the window will start being more than 45 minutes away. By the time it gets to maybe 10AM the window will be over two hours away. By Noon the window will be maybe 6 hours away. The final FPs given out (at maybe 2PM on a busy day) will be for near park closing - 9-10 hours away.
So even if you can get a SM FP at say 1PM, the return window may not be until 9 or 10PM that night which may or may not fit your schedule that day.
Bottom line? Get to the park early and get your SM FPs first thing.
I wrote up a guideline to DLR FP and it is a very popular link around here:
See "Getting the Most Out of FastPass During High Season"
http://www.disboards.com/showthread.php?t=885132
Here is another link on how early FP collecting can affect your day:
http://www.disboards.com/showthread.php?t=1107718 - check out my post #4 in that thread.
One extremely useful tip about DLR FastPass. They have a policy to not enforce the end of the FP window. So if your SM FP window is for say 1-2PM, you can use it
any time after 1 PM that day. To drive the point home, one day last summer I got a SM FP right after 8AM. The return window was 8:55-9:55AM. We did not use it until 11:45PM that night - 12 hours late. And the standby line at midnight was 100 minutes long. 100 minutes!
I have used late FPs at DLR dozens of times without ever a question.
Finally, if you feel like you need help getting a smart ride schedule, invest $15 in RideMax (
www.ridemax.com ). I use RideMax itineraries from time to time myself.