Sure! I'm surprised you can't reproduce, it happens 10% - 15% of the times.
Here's a simple repro:

-Rez a box
-Add a default script
-Recompile it a couple of times
-When it doesn't say "Hello, Avatar!" close the script and open it again.

At the office hour on friday 16th we showed it to Vektor, and he reproduced it within a minute.
Also on friday Yumi said:

"Yumi Murakami: when I detach an attachment with a running mono script, sometimes the script goes back to non-running and non-mono."

I've tried this. It took about 20 times of reattaching, but sure enough, the script stopped running, the Mono-box unchecked.
Only recompiling gets it running again.

=======

Second Life 1.20.6 (87323) May 12 2008 17:18:14 (Second Life Mono)

You are at 255832.9, 255380.0, 21.5 in Sandbox Cordova MONO located at sim3001.aditi.lindenlab.com (8.2.33.227:13000)
Mono 1.21.1.87548

it started when we got the new viewer: "Second Life 1.20.6 (87323)"

here's a way of reproducing it fast:

Using the viewer: "Second Life 1.20.6 (87323)"
Create a new object
create a new script that contains this:

default
{
state_entry()

}

Check the mono box, and save it, normally you should get the message "I am running"

now re-open it.

edit it ( add an space ) and save it again

you should get a new "I am running" message, then do it again... and again... and again...

at one time or another ( mostly sooner ) you will never get the "I am running" message.

then if you re-open the script, you will see that the "Running" checkbox is unchecked !
And also sometimes the "mono" checkbox is uncheched as well !

now, this is not the same, and this was reported to vektor, by myself using a notecard ( he told me he was going to file a Jira about it, but I have not checked it )

this exact same behavior but randomly shows when you have an object with multiple scripts, and yo go to:

Tools - Recompile objects in selection - Mono ( or LSL )

Some will end up running, others will loose the running bit, others where in mono now they will loose the mono check, etc, that part the running and the mono check just goes away, and it is becomming a real issue and problem when beta testing scripts. Vektor is well aware of the problem, he can do a much better explanation than me or anyone else.

thx Scouse

Teleporting
Region crossing
Recompiling to mono

I added this to seven scripts in a prim for a simple repro, incrementing scriptnum for each new script:

// <Code>
integer scriptnum = 1;

default {
state_entry() { llSetTimerEvent(3.0); }

timer() { llOwnerSay ("Script " + (string)scriptnum + " still running"); }
}
// </Code>

Setup:
Start in a Mono region with another Mono region next to it. For this test, I started in Sandbox Cordova MONO.

Repro:

1) Add the above script to a prim 7 times, increment the scriptnum and save to mono for each.
2) Make 3 copies of the prim and name them 1, 2 and 3. If you want, take a copy of one for later testing.
3) Recompile prim 1 to mono. Do so until at least one script stops reporting. This usually takes no more than a few attempts.
4) Attach prim 2 and walk from one Mono region to another. Do so until at least one script stops reporting. This usually takes no more than a few attempts.
5) Return to the place where you created your prims, and drop prim 2.
6) Attach prim 3 and teleport to another Mono region. Do so until at least one script stops reporting. This usually takes no more than a few attempts.

Results: Scripts are frequently being set to Not Running, as well as having their Mono bit toggled off. LSL2 compiled scripts seem to be ok.

Expected Results: Mono scripts should be able to go through the above steps and remain running Mono scripts.

After manually recompiling all scripts and activating them... testing and working fine... then take the object back to inventory... rez again and randomly scripts are disabled and mono turned off again.

There was nobody in the sim (cordova) and therefore sim load seems to have nothing to do with it.

I may be wrong but I have the impression this was NOT happening a month ago.

Phew