Keep Alive in .htaccess
I can't see any potential issue with using Keep-Alive unless it is not properly configured. e.g


​KeepAliveTimeout value is not ideal. For example, if the site is high traffic the value should be higher​ to make sure there is no frequent tcp connection re-initiated.
​MaxKeepAliveRequests should be tweak according to number of assets the server is serving.


It is recommended to use this feature to:


Reduce latency
Reduce the use of server resources such as CPU and memory


For HTTPS you might want to check SPDY.


  ​SPDY is a protocol developed by Google to increase the speed and
  efficiency of delivering web content. SPDY modifies parts of the
  HyperText Transfer Protocol (HTTP) to improve web performance.