Finally I found the solution. The reason of the problem was a stupid mistake.
Shortly: using var_export in a cycle, and giving its converted return result to the db_query function as a parameter.

Longer explained:
There is an enum field in my own MySQL table, which looks like this:

`is_own` enum('true','false')

So true or false values were stored as a string, this way there were only these two possible values to set. It could have also been set as 0 or 1 (or enum('0', '1') is another possible solution), but this way I thought it will be simpler to read later, and I limited the opportunities to just two values.
To pass a boolean value to db_query(), firstly I had to convert it to a string, so for example the false value (as a boolean) had to be converted to "false" (as a string), not to be casted later to 0 (because if it's casted, the update doesn't affect any rows, since for example 'false' (as a string) isn't equal to 0 in a MySQL-query). To do this, I used the following code snippet (using var_export):

$is_own = false;

$is_own = var_export($is_own, true);

This normally works perfectly (so it converts boolean true to string "true"), BUT the problem was that for some stupid reason I put this conversion in the cycle like this:

$is_own = false;

// ....   

foreach($blabla as $index => $value){

    // here's the mistake...!
    $is_own = var_export($is_own, true); 

    // ....
    $query_result = db_query( $query,
        $value,
        $prev_value,
        $other_field_value,
        $is_own // <--- !!
    );
    // ....
}

so this way $is_own variable's value (false) was converted in every cycle step like this:

1. 'false'
2. '\'false\''
3. '\'\\\'false\\\'\''
4. '\'\\\'\\\\\\\'false\\\\\\\'\\\'\''
5. etc........

This way it's not a miracle that all of my UPDATE querys were executed successfully, but only the first resulted in some affected rows...
After some headbanging, I put my var_export function outside the cycle (before foreach), and now everything works perfectly. (This would be a bigger job to modify the field to INT values (0, 1), so I leave it this way.)

Anyway, thanks.

Finally I found the solution. The reason of the problem was a stupid mistake.
Shortly: using var_export to convert a boolean value to string (false ==> "false") in every cycle step, and giving its each time converted return result to the db_query function as a parameter.

Longer explained:
There is an enum field in my own MySQL table, which looks like this:

`is_own` enum('true','false')

So true or false values were stored as a string, this way there were only these two possible values to set. It could have also been set as 0 or 1 (or enum('0', '1') is another possible solution), but this way I thought it will be simpler to read later, and I limited the opportunities to just two values.
To pass a boolean value to db_query(), firstly I had to convert it to a string, so for example the false value (as a boolean) had to be converted to "false" (as a string), not to be casted later to 0 (because if it's casted, the update doesn't affect any rows, since for example 'false' (as a string) isn't equal to 0 in a MySQL-query). To do this, I used the following code snippet (using var_export):

$is_own = false;

$is_own = var_export($is_own, true);

This normally works perfectly (so it converts boolean true to string "true"), BUT the problem was that for some stupid reason I put this conversion in the cycle like this:

$is_own = false;

// ....   

foreach($blabla as $index => $value){

    // here's the mistake...!
    $is_own = var_export($is_own, true); 

    // ....
    $query_result = db_query( $query,
        $value,
        $prev_value,
        $other_field_value,
        $is_own // <--- !!
    );
    // ....
}

so this way $is_own variable's value (false) was converted in every cycle step like this:

1. 'false'
2. '\'false\''
3. '\'\\\'false\\\'\''
4. '\'\\\'\\\\\\\'false\\\\\\\'\\\'\''
5. etc........

This way it's not a miracle that all of my UPDATE querys were executed successfully, but only the first resulted in some affected rows...
After some headbanging, I put my var_export function outside the cycle (before foreach), and now everything works perfectly. (This would be a bigger job to modify the field to INT values (0, 1), so I leave it this way.)

Anyway, thanks.