Many different things can cause constant panting. Heavy panting can be caused by heart problems, lung problems, fever, or bronchitis. You can read about this here: http://www.petplace.com/dogs/panting-in-dogs/page1.aspxDogs pant for various reasons. They pant to cool down, but they also pant when they are under stress, in pain, or afraid. There can also be medical causes such as neurological problems, respiratory disorders, and Heart problems such as heartworm, anemia, and fever.If your dog is panting but has no other symptoms, keep a watch on him. If it still seems excessive after a day or so, or if he develops more symptoms, I'd schedule an appointment with your Vet.As for when is it time to say goodbye to your pet, that is a judgement call. If your dog is not in constant pain, still has some activities that is enjoyed even if your dog may move a little slower and seems content to just lay by your feet, then I'd say your dog still has some quality of life. If your dog can no longer do anything that used to be enjoyed and you can see that your dog’s eyes are pain filled and sometimes even your touch doesn't give comfort, then it probably is the right time.So if you feel the panting might be due to pain or if there are other symptoms you didn't mention, then have your dog ssen as soon as possible. Otherwise, keep an eye on her and have him seen if the constant panting continues. I hope this information is helpful to you.I hope this information is helpful to you.
I might be able to add a bit more information for you in addition to what was mentioned above. In an older lab, there is something called Cushing's Disease that is very common. It is a disease of the endocrine system, and basically it causes the body to release more steroid. This steroid, among other things, causes these dogs to pant constantly and excessively, mainly because they feel hotter than usual (even if their temperature is normal). This can be treated, but it is typically expensive, so if you cannot afford it I would probably not do anything (if this is what is wrong with your dog).
Another cause for panting would be severe pain, which can be caused by spinal problems such as a slipped disc, or by internal pain caused by something like pancreatitis. These things would typically cause your dog to not want to eat, act lethargic, etc. So if your dog is acting totally normal, but is just panting, then I would guess your dog is not in pain, and it is more likely Cushing's disease. There isn't anything you can do at home for Cushing's disease, but the good news is that it isn't typically painful or uncomfortable, so your dog can continue to live with it.
Without seeing a vet, it is impossible to say for sure what the cause is, but I hope this helps. Once your dog stops wanting to eat, that is usually a good sign that he is uncomfortable and it might be time to put him down.
Best of luck.