This is a topic I am going to revisit today.
BJJ is not a team sport, and after every match there is always a winner and a loser. But really, you can not always be the winner, and when you are beginning (or train with more advanced/heavier partners), it is often the case.
How do you stay motivated during this period?
In my opinion a few things help:
1) Having new training partners come by time to time
2) Spend time (a lot) watching high level matches on video and/or instructionals
3) Spend more time drilling to make sure that the technique is perfect. Ask a higher belt to watch and make sure this is the case.
now an amazing video released by budovideos: the mendes brothers