Hi, welcome to the forum.

In the Write Screen do you have Adsense ticked in the list of "Text Renderers" on the right hand column beside the posting area?

Yes, I have it under the Text Renderers and it is check by default.

What version of b2 are you using?

Try going to the Tools tab then misc and click on "delete pre-rendered item cache". It sometimes gives unexpected results !!!
In the settings for the Adsense Plugin, does your Adsense code look like this dummy of my Adsense entered in my Adsense Block input.....

<p class="money"><script type="text/javascript"><!--
google_ad_client = "pub-1234567891122334";
google_ad_width = 468;
google_ad_height = 60;
google_ad_format = "468x60_as";
google_ad_type = "text";
google_ad_channel = "";
google_color_border = "BBBB99";
google_color_bg = "EFEFCC";
google_color_link = "DD9955";
google_color_text = "777777";
google_color_url = "777777";
//-->
</script>
<script type="text/javascript"
  src="http://pagead2.googlesyndication.com/pagead/show_ads.js">
</script></p>

I am using version 1.10.2. I just started and was able to install the script because the hosting company installed it otherwise I am new to computers.

My adsense looks like this

<script type="text/javascript"><!--
google_ad_client = "pub-1234567891122334";
/* 728x90, created 3/23/08 */
google_ad_slot = "123456789711";
google_ad_width = 728;
google_ad_height = 90;
//-->
</script>
<script type="text/javascript"
src="http://pagead2.googlesyndication.com/pagead/show_ads.js">
</script>

Then you put this in the textbox at the settings for the Adsense plugin:

<div style="float:right; clear:both; margin:5px;">

<script type="text/javascript"><!--
google_ad_client = "pub-1234567891122334";
/* 728x90, created 3/23/08 */
google_ad_slot = "123456789711";
google_ad_width = 728;
google_ad_height = 90;
//-->
</script>
<script type="text/javascript"
src="http://pagead2.googlesyndication.com/pagead/show_ads.js">
</script>

</div>

Good luck

Tried that and nothing happened. Maybe I will try to upgrade and see if that helps.