Bitcoin Forum

I had this issue hundreds of times. whenever I reply to a thread I found that the person is no more online but status keeps showing that green sign(Online status) for quite long time. It should be in real time.

Well I suppose someone could just leave the page open and walk away.... I disable it because I don't want people thinking I'm "online" when I'm not for this very reason. :P

You need to better understand what "online" on a regular website is.
Any user interacts with this forum (and therefore the forum knows he's still there) only when a link is clicked. The forum then sends the newly requested page and logs the activity.

Then the user reads the page for several minutes without asking for a new one. The forum doesn't have any idea whether the user is still there reading or if he already went to another site or closed the browser. The best it can do is "guesstimate" the user is there for about 15 minutes. So it marks the user as offline after 15 minutes of the last interaction.

For the online status to be "real time" a background (jQuery or similar) process would have to be querying the forum all the time, and it would need to keep updating the DB all the time. What a waste of bandwidth and mainly server's processing power!

The best you can do is check the user's "Last Active" time rather than the Online status and draw your own conclusions.

I think it's real time, maybe the only thing that is not real time is when someone send a new message or post because it needs to refresh the page to load it.

In idea it's real time but it doesn't refreshes statistics in every second and that also would take a lot of server resources.
On another side even FB doesn't shows in real time, for example when I close it, I am still shown online for 1-2 minute.
Hope that's not a big deal for you, forum doesn't needs to waste resources on that function.