Not a single regex but one way to do what you want is to read your file in paragraph mode, with $/ and split the logic:

{
  local $/ = ""; # Edit: added use of local for good practice

  while (<DATA>)
  {
    s/^##.*//s unless /^\w/m;
    print;
  }
}
__DATA__
## Remove

## Keep
this

## Remove

## Also keep
that
[download]

Otherwise you could use a negative look ahead assertion (?!^\w)

Edit: seems like I really didn't read the requirement well enough ^^"