Items not Updated During Cron run

I need to update each feed manually on the aggregator summary page (/admin/content/aggregator_summary). First I must remove the old item, then add the item to get updated feed item on my site. Prior to doing this, when I click on feed title from the aggregator summary page, it shows the old item. When I click on the feed icon, I see the new item in the feed.

I thought the clearing of the old item and the replacement with the new item was handled in the cron run. The items are showing that they are updated on the aggregator summary page, with each cron run, but they are not really being updated on my pages. Do you have any suggestions?