Call it Puppy Love | Family-raised Chihuahuas | Puppy Tips
Your puppy wants to be with the rest of the 'pack' at bedtime. This behavior is highly adaptive from the standpoint of dog behavior. When a puppy becomes separated from its pack it will whine, thereby allowing it to be found and returned to the rest of the group. This is why so many books on puppies and dog behavior strongly recommend that you allow your puppy/dog to sleep with you in your room to reduce the liklihood of crying at night.
Try moving the crate into your bedroom. If your puppy whines, first make sure it doesn't have to go outside to eliminate. This means getting up and taking it outside. If it whines again, or doesn't need to go outside, say something like 'NO, SLEEP' or 'NO, QUIET'. If the puppy continues to whine, then simply ignore any continued whining. If you don't reinforce the whining by comforting it (other than to take it outside — which is OK), it will eventually learn to settle down. Also, be sure to have a vigorous play session during the evening. This should tire the pup out and it will sleep much more soundly.
We choose to crate but if you are opposed to crating, you can designate a spot for your puppy on the bedroom floor. Keep the door closed and/or put a leash on it to keep it close to the bed. When it whines or moves about, take it out to eliminate. Otherwise, as above, say 'NO, SLEEP'.
Puppies that cannot sleep in the bedroom (for whatever reason) may be comforted by a ticking clock nearby, and a clothing item of yours from the laundry. But not an item you adore, as they might give it a bit of a chew.