Is it a software or a hardware problem with the Colorsource 20?

"the light will stay on", meaning the channel's fixture and/or dimmer will remain illuminated in it's last set state?

This sounds like a property of the fixture or dimmer. If you disconnect the DMX cable from the fixture, does the fixture also remain on, in it's last set state?

With a ColorSource 40 AV, and the dimmer left on (while hibernating) for my connected Chauvet SlimPAR Pro H, I see... The SlimPAR indicating DMX signal has gone away, and the fixture stays illuminated in it's last set state. I see this exact same fixture behavior if I disconnect the DMX cable.

When the DMX cable is disconnected the light goes out.

Hi,

I have a 20 as well and whenever the console is turned off, our Colorsource pars will turn on and stay on.

Like jbehrle mentioned 

Earlier, the lights are just like "I need DMX" and the behavior of them is normal. It happens all of the time at my school with our Colorsource.

Hi,

I have a 20 as well and whenever the console is turned off, our Colorsource pars will turn on and stay on.

Like jbehrle mentioned 

These are features of the fixture, not the console.

When the console is hibernating, it stops sending any DMX and gently biases the DMX line "positive" as required by the RDM standard.
This ensures there's no flicker, and allows any inline controllers (eg architectural button stations) to send their own DMX and/or other proprietary protocols down the wire. We have had a few reports of devices that appear not to detect DMX properly so don't treat this as "no data", despite what the standards say

1) Most DMX fixtures do one of the following "some time after" after DMX stops:

• Turn off
• Hold-last-look forever
  • The fixture keeps doing whatever it was doing when DMX stopped, until DMX starts again.
• Play an internal Preset or Sequence
  • Sometimes they also send data along the DMX line to synchronise with other fixtures

Many fixtures allow you to configure which of the above to do.
Some even allow you to configure how long they will wait before turning off or playing the internal preset/sequence.

For example, you can configure the ColorSource Par to play a Preset or Sequence when DMX is lost.
With no DMX, use the buttons on the back to play the Preset/Sequence you want (or off!).

It will then return to that same internal Preset/Sequence every time DMX is lost.

2) The console will send the Home values for all patched fixtures when it loads the showfile.
If that's not "all-zero-dmx", then the fixture will probably move or change internal colour.

Fixtures that have 'non-standard' Intensity functions such that DMX@0 is not "off", are likely to produce some light while Homing.
In most cases you'll never see that oddity when actually using the lights as ColorSource tries very hard to make everything work in almost the same way.

Still having problems with the ColorSource 20. Last show all 5 spot lights stopped working, reset the faders and after a few minutes they stated working again. One elation spar light that was not being used came on and stayed on all show had the physically disconnect power after the show. One Elation FuzePar stopped working for a while then started working. So how can we fix the problem?