First off, there may be metal shielding somewhere. Cellphones send their data with electromagnetic waves (in the microwave spectrum I believe). For certain reasons that I won't really go into (but basically for a charged object, its charge is on the surface), electromagetic waves cannot pass through into a metal box. This is why you won't get a signal in a lift (elevator you may call it), unless the lift has a receiver inside the lift itself.
If you basement is covered by a layer of metal above, then the signals will have a hard time getting through.
Like everything however, they do lose energy. Going through thick things takes more energy than less dense things (its harder for you to swim through treacle than water); so getting through a lot of thick brick/stone (which your basement may have) can also be a challenge for it.