Many people have dogs that can't seem to be house trained, even after a year or more of trying.
Some breeds have reputations for being difficult or impossible to potty train: Beagles, Chihuahuas, Dachshunds, and others. Generally, small dogs do seem to have a harder time learning house training than larger dogs, but no healthy dog is impossible to potty train! That bears repeating:
No healthy dog is impossible to potty train!
The training method is the same, regardless of the breed, age, or size of the dog being potty trained. However, for small or tiny dogs, such as a Chihuahua, there are a few minor tweaks to the potty training method, basically in order to consider their size.
One consideration that is often left out of the potty training equation is the human factor. The human is actually in complete control of the house training process, not the dog! So that would tell you who has the responsibility for making it work. In fact, you are 100% responsible for your dog's potty training success (or failure).
That is important to remember, so that you don't end up trying to blame the dog, or the dog's breed, or the dog's size, if you fail to complete the potty training. If you are having trouble, and wondering if your dog can really be potty trained, go back and read the statements in bold.
Here is the basic housetraining method for any dog, no matter the age or the size:
it was written for house training a Chihuahua or other very small dog, but again, the method is the same, and only the time needed for completion and the intervals between potty breaks are adjusted to make this work for any breed, any age, any size, no matter how stubborn you believe your dog to be.
If you apply this method and it doesn't work, then you need more one on one help to find the real problem (usually completely different from what you expect).