I had to cross a sim border over 20 times to get it to fail.

The following is some code I was running in an attachment:
integer count = 0;

timeloop() {
integer i;
llResetTime();
for ( i=0; i<10000; i++ );
llSetText( (string) count++ + ": " + (string) llGetTime() + " \n \n \n \n \n \n \n \n", <1,0,0>, 1 );
}

default {
state_entry() { llSetText( "test", <1,0,0>, 1 ); timeloop(); llSetTimerEvent( 0.1 ); }
timer() { timeloop(); }
}

It is important to note that I see this behaviour in scripts not in attachments.

A more complex case is the Dominus Shadow (a car I made). It's a vehicle that is not attached.

Crossing the sim border caused it to fail with very many error messages (Can't repro at the moment):
[14:16] Object [script:Hydraulic Script Rot.Front]: Script run-time error
[14:16] Object [script:Hydraulic Script Rot.Front]: System.Runtime.Serialization.SerializationException: serializationStream supports seeking, but its length is 0
at System.Runtime.Serialization.Formatters.Binary.BinaryFormatter.NoCheckDeserialize (System.IO.Stream serializationStream, System.Runtime.Remoting.Messaging.HeaderHandler handler) [0x00000]
at System.Runtime.Serialization.Formatters.Binary.BinaryFormatter.Deserialize (System.IO.Stream serializationStream) [0x00000]
at LindenLab.SecondLife.Script.Deserialize (System.Byte[] object_data) [0x00000]
at LindenLab.SecondLife.Script.Deserialize (System.Byte[] class_data, System.Byte[] object_data) [0x00000]

[There are many similar error messages]

I would be glad to provide a copy of the Dominus Shadow for testing - I haven't been able to get a simpler case to fail in the same manner.

[7:18] emDash [script:-Portals-]: Script run-time error
[7:18] emDash [script:-Portals-]: System.Runtime.Serialization.SerializationException: serializationStream supports seeking, but its length is 0
at System.Runtime.Serialization.Formatters.Binary.BinaryFormatter.NoCheckDeserialize (System.IO.Stream serializationStream, System.Runtime.Remoting.Messaging.HeaderHandler handler) [0x00000]
at System.Runtime.Serialization.Formatters.Binary.BinaryFormatter.Deserialize (System.IO.Stream serializationStream) [0x00000]
at LindenLab.SecondLife.Script.Deserialize (System.Byte[] object_data) [0x00000]
at LindenLab.SecondLife.Script.Deserialize (System.Byte[] class_data, System.Byte[] object_data) [0x00000]