Here is a looper to remove more than one consecutive blank lines, which illustrates the concept:

Code:

sed '
  :loop
  $b
  N
  s/^\n$//
  t loop
  P
  s/.*\n//
  b loop
 '

I put my sed script on its own lines for clarity. If you want to check for lines with only spaces and tabs, that scrubbing can be done upstream in one line or inserted here as two lines. That is why I say sed loopers are usually best kept separate from non-loopers. There is no single place to filter and translate single lines in a looper without redundant processing, like substituting on each line twice.

Narrative: