Greetings,
Though there are many things that could be suggested about your code the most important is to adopt the use of strict and warnings.
Other than that I get the feeling you have not provided all of the relevant code in the example you give.

For instance where do %loop_data and $loop_data get initialized? What is suppose to happen to ($name,$value) in your

foreach $line (@allow_edit){ .... }
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block?
I think I follow what you are attempting up until you close your filehandles... Then things get murky.

Empirically @loop will never hold anything since you never fill it. Your #fill in the loop, foreach block creates and fills in $name and $value that fall out of scope with each iteration, @loop is never involved.
Now if I follow your intent, and this is a big stretch to say the least, here is my suggestion for what I think you are shooting for (However not having seen your HTML template its a guess at best).

Untested mind you.

my @loop;
#fill in the array @loop with hash references from @allow_edit...
foreach (@allow_edit){ 
    my($name, $value) = split /=/,$_; 
    push @loop, {$name=>$value};
}
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Then continue with your template calls.
It would be helpful to see what the markup (HTML) looks like that you are filling with "loop" in your $template->param call.
without that everything is simply a shot in the dark.

---

Update
Okay, thats definitely helpful.
So given the code.

<!-- start of loop -->
<TMPL_LOOP NAME="loop">
                <tr>
                        <td align="right"><TMPL_VAR NAME="part1"></td>
                        <td><INPUT TYPE=text NAME="<TMPL_VAR NAME="par
+t1">" VALUE="<TMPL_VAR NAME="part2">"></td>
                </tr>
</TMPL_LOOP>
<!-- end of loop -->
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I am lead to think you would like $name to appear in "part1" and $value to appear in "part2". Am I getting warmer?
Lets modify the loop I suggested earlier to accomplish this.

my @loop;
#fill in the array @loop with hash references from @allow_edit...
foreach (@allow_edit){ 
    my($name, $value) = split /=/,$_;
    push @loop, {part1=>$name, part2=>$value};
}
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That should do it. I hope that helps.
And one more thing, have a look at the range operators for another way to handle your file partitioning.

-InjunJoel