I have never had the problem on this board but on more than a couple others I get exactly what you are talking about, and it is not due to replying and deleting or editing.
Your internet exploder or whatever has some internet options and stuff. You want the browser to refresh every time you click on a page, otherwise you are loading from cookies and memory or where ever and get what you have read in the past.
Changing this setting never cured my computer completely. I still sometimes need to hit the refresh button. And sometimes it takes two or three refresh hits to get to see the new posts.
Clearing cookies, history, temp files, and that sort of thing helps.
Setting the browser settings helps.
Using refresh also helps.
I have found nothing that solves it. But the refresh allows me to eventually read it.
Now I have no clue about the posting and deleting, but with some of the nuts on this board it is entirely possable they are the cause.