Having used turbotax for years, does turbotax remember my capital losses from previous years and applied them in the current year or do I need to keep track?

If you entered you information correctly when you began to use TurboTax, it will  compute and carry forward you capital gains and or losses on a continuing basis.

The carryforward worksheet is one of those that you need to keep with your important tax records. anything can happen and you may not use TurboTax forever.