If I install new version of Atahualpa I almost always forget to renew counter code in header.php
Have you some opportunity to insert counter code one time (into some field) that at updating of new version this code would not erased.

You can generally add code to someplace in the theme options. Then you will be all set after an upgrade.

what type of code is it, have you looked at the 'Add HTML/CSS Inserts' options?

This code:
<!-- Histats.com START (hidden counter)-->
<script type="text/javascript">document.write(unescape("%3Cscript src=%27http://s10.histats.com/js15.js%27 type=%27text/javascript%27%3E%3C/script%3E"));</script>
<a href="http://www.histats.com" target="_blank" title="track hits" ><script type="text/javascript" >
try {Histats.start(1,1174717,4,0,0,0,"");
Histats.track_hits();} catch(err){};
</script></a>
<noscript><a href="http://www.histats.com" target="_blank"><img src="http://sstatic1.histats.com/0.gif?1174717&101" alt="track hits" border="0"></a></noscript>
<!-- Histats.com END -->

I always insert it in Header.php at the bottom

see ATO->Add HTML/CSS Inserts->HTML Inserts: Body Bottom

I noticed when I install new Atahualpa version then my counter code in this field - HTML Inserts: Body Bottom was erase again. And I insert the code again manually. So this field is erased at new version installation.

From what version to what version?

from 3.2 to 3.6.4

That was a BIG jump in versions. I think you should be ok from now on.