Yes there can be a problem like this because of parent leaving for work, loneliness,or you just said that the loss of a companion, attention. So the question is how can we prevent depression in our pet? Here is the good news that many pets can overcome depression on their own. Offer them more attention as possible to you one by one if you don't have full time. Keep them engage with regular activities. If your think they experiencing depression due to the loss of companion, then get another pet which convenient to you.