There comes a time in pretty much every dog's life that he will not take a given command. The reasons for this are numerous, ranging from just an age related phase, not adequate training, fear, or just simple distraction issues. The first step a frustrated owner should take is to try to assess WHY their dog is not taking a command, as the solution differs for each reason.
Age
Just like human babies, puppies go through quite a few learning stages. For example, puppies have an ideal socialization "window" before 12 weeks of age where they are very accepting of new places, people, sounds etc. After 12 weeks of age, pups become more aware and skeptical of their surroundings and socialization doesn't come as easily. Pups also go through several fear phases where they are suddenly frightened of things that didn't bug them before! When adolescence approaches, many pups go through a period of rebellion. Usually this is when a pup that was well trained seems to not have any training at all! This stage occurs most often between 6 and 18 months. What is going on? For dogs that are not altered, this is the time of sexual maturation and the hormones and drive that go along with that create a dog that is less inclined to listen to his owner. Even altered dogs are going to have attention issues because there is a whole world out there that he has just discovered! Follow instinct is now gone and most pups no longer have the desire to stick near their owner when there is action going on. The solution to this issue is to go back a little bit with training. Be sure to proof commands in order of less distracting environments first (house, yard, front yard, neighborhood, empty park, slightly busy park, friend's house, dog park). If your dog cannot listen to your command in the backyard, he surely cannot listen at the dog park! During this time you may have to use high value treats, start incorporating play-training, and even take a look at a "Nothing In Life is Free" protocol.
Not Fully Trained
Some dogs aren't listening simply because their owners have a misunderstanding of how well they trained their dog. If the dog has a so/so recall in the yard, expecting him to come at the park is just silly. Humans feel embarrassed and tend to ask too much of their dog when in public places (such as the park, pet store, vet or groom shop). Getting frustrated that their dog won't sit at the vet when he has to be told and lured at home is the owner setting the dog up for failure. The solution is to simply not ask the dog to things he is not capable of doing and go back and do more training!
Fear
Every dog is going to have a fear of something or someone in their life. Dogs are not very obedient when afraid, and for good reason! They are worried about themselves and there are chemical reactions and bio-feedback going in in their brain that makes it extremely difficult to listen to what the human is saying. During a small fearful event such as visiting the vet, the best solution is to just be comforting and understanding. Don't ask your dog to sit, stay etc. when he is terrified of anything, and do not force a position especially! If the fear is an ongoing thing of something that is a regular occurrence, seek training help to start a counter-conditioning and desensitizing program.
Distraction
Distraction goes back to a dog that doesn't have adequate training. I hear all the time from clients, things like, "My dog listens great, till he sees a squirrel!" My reply usually is that my dogs don't have issues with squirrels or prey animals or food dropped because I worked on it. I systemically worked up to each distraction level with each command essentially. Distractions can be objects, people, animals and even environments. To work on distractions, start with something like can my dog sit in the kitchen with no distraction? Yes, then move onto asking for a sit in the kitchen with people milling about, family members talking, eating, throwing a toy to each other. Move out into the yard and start over with minimal distractions and work up again. Do the same in each new environment. When you add an aspect, you must go back a little in another area, meaning if your dog can sit in the most distracting environment you can think of, don't suddenly switch gears to asking for a down stay in that same environment if you haven't worked on the down stay in the lower distraction scenarios first.
Pain
Lastly, there are times a dog doesn't listen because he is in pain and the owner is not aware. This can obviously happen at any age, but senior dogs are more likely to have pain related to unseen issues like arthritis. My own dog refused to hold a down on hard surfaces for about a month and I was pressuring her and working on it till I realized she will hold a down for a long time on any soft surface. When it occurred to me that she was around 7 years old, it was winter and her joints were bugging her, I put her on some joint medication, gave her a little break and she was back to holding downs on any surface. Listen to what your dog is telling you! A well trained older dog proofed with distractions that isn't showing fear, most likely has a very good reason for not complying with a command.
So remember, dogs don't just "blow you off" for no reason. Find the reason and remedy it, and your dog will be back to listening in no time (or as much time as it takes to fix)!