While there is no easy answer to this question, there are a few criteria that will help guide you in the right direction. Because our pets are genetically programmed to hide weakness, we do need to be diligent in looking for negative life quality indicators.
Severe pain is perhaps the most common reason owners face this decision; however, there are many other factors that contribute to their well-being. When our animals lose their appetite for more than an isolated day or two, this is a clear indication that they are feeling very poorly. Furthermore, when they seem to be less interested in normal behavior like going outside to play or going to the bathroom and seem reluctant to interact with you in a normal way, they are letting us know about their discomfort. If their movement is so compromised that they must eliminate on their bedding, this causes physical and emotional distress for them and should be considered a negative variable as well.
Many owners ask about whether their pet is in pain and seem to focus on this question to help them make the choice. What is truly important to realize is that pain is not the only reason for a negative life quality; being uncomfortable can result from pain, weakness, decreased appetite, nausea, lack of mobility, and many other situations. The best time to help your baby is when the bad days outnumber the good ones; try your best to avoid waiting until you no longer see any positives.
While we do occasionally see some pets pass naturally without assistance, hoping for this usually means a fair amount of suffering in the meantime.