Nintendo DS only recognises game if inserted when I power on
Solution 1:
Tested on my own DS Lite, which is "tried and true" (I think I got it in the summer of 2007, and it still works perfectly fine, never crashes or anything), and yes, the DS Lite does not support hot swapping (unlike, say, the 3DS).
Solution 2:
I'm 95% sure the DS Lite doesn't support "hot swapping" like this, I had a unit for two years but lost it. I am 100% certain my Nintendo DS ("fat") does not support hot swapping cards, and I'm pretty sure the DS Lite functioned exactly the same in that regard. Both DS game cards and GBA carts had to be inserted before the console was powered on to be recognized. (and popping the card out in gameplay almost always results in an unrecoverable crash)
Hot swapping's pretty new to handhelds; I think the PSP was my first one that did it.
Solution 3:
I have both a DS Lite and a 3DS; the DS Lite does not support "hot-swapping" (removing, but mainly inserting a game whilst at the DS' [any DS, not just the orginal] start up [or, main] menu), whereas the 3DS supports hot-swapping for both 3DS and original DS games.