Perl 5, 27 32 22 bytes

{{open my$h,'>o'}redo}

If simply changing the modification timestamp of a file suffices...

Quick explanation:

{ # Braces implicitly create/mark a loop.
    { # New, more localized scope, for `my` variable.
        open my $filehandle, '>', 'o';    # Writing to file "o".
        # close $filehandle;   # Called implicitly when
                               # variable gets destroyed.
    } # Scope gets destroyed; so does $filehandle.
    redo; # ...the loop.
}

Previous solution (32 bytes): {{open my$h,'>o';print$h 1}redo}

Edit: {open F,'O';print F 1;redo} ← Didn't test the code before posting; now I had to correct it.

Perl 5, 27 32 22 bytes

{{open my$h,'>o'}redo}

If simply changing the modification timestamp of a file suffices...

Quick explanation:

{ # Braces implicitly create/mark a loop.
    { # They also create closures, for `my` variables.
        open my $filehandle, '>', 'o';    # Writing to file "o".
        # close $filehandle;   # Called implicitly when
                               # variable gets destroyed.
    } # $filehandle gets destroyed because there are no references to it.
    redo; # ...the loop.
}

Previous solution (32 bytes): {{open my$h,'>o';print$h 1}redo}

Edit: {open F,'O';print F 1;redo} ← Didn't test the code before posting; now I had to correct it.

Perl 5, 27 32 bytes

{{open my$h,'>o';print$h 1}redo}

Quick explanation:

{    # <-- Braces implicitly create/mark a loop.
    {    # <-- New, more localized scope, for `my` variable.
        open my $filehandle, '>', 'o';      # Writing to file "o".
        print $filehandle 1;    # Yes, no comma there!
                                # Search "Indirect Object Notation".
        close $filehandle;    # Called automatically when the
                              # variable gets deleted.
    }    # <-- Scope gets destroyed.
    redo;  #...the loop!
}

Edit: {open F,'O';print F 1;redo} ← Didn't test the code before posting; now I had to correct it.

Perl 5, 27 32 22 bytes

{{open my$h,'>o'}redo}

If simply changing the modification timestamp of a file suffices...

Quick explanation:

{ # Braces implicitly create/mark a loop.
    { # New, more localized scope, for `my` variable.
        open my $filehandle, '>', 'o';    # Writing to file "o".
        # close $filehandle;   # Called implicitly when
                               # variable gets destroyed.
    } # Scope gets destroyed; so does $filehandle.
    redo; # ...the loop.
}

Previous solution (32 bytes): {{open my$h,'>o';print$h 1}redo}

Edit: {open F,'O';print F 1;redo} ← Didn't test the code before posting; now I had to correct it.

Perl, 27 bytes

{open F,'O';print F 1;redo}

Expanded version:

{    # <-- Braces implicitly create a loop.
    open FILEHANDLE, 'O';
    print FILEHANDLE 1;
    redo;  # Redo the loop code.
}

Perl 5, 27 32 bytes

{{open my$h,'>o';print$h 1}redo}

Quick explanation:

{    # <-- Braces implicitly create/mark a loop.
    {    # <-- New, more localized scope, for `my` variable.
        open my $filehandle, '>', 'o';      # Writing to file "o".
        print $filehandle 1;    # Yes, no comma there!
                                # Search "Indirect Object Notation".
        close $filehandle;    # Called automatically when the 
                              # variable gets deleted.
    }    # <-- Scope gets destroyed.
    redo;  #...the loop!
}

Edit: {open F,'O';print F 1;redo} ← Didn't test the code before posting; now I had to correct it.