Well, i called the house where the power strip is and found out the prongs are in the power strip which is a separate piece. 

I did not know it did that, I could have lost that thing forever, what a stupid feature. There should be 2 separate plugs for different power sources imo.

The prongs on an official Yamaha Modx power supply should be permanently attached to the power supply.

Are you perhaps using a 3rd party power supply instead of the official one? If not your power supply is broken and should be replaced.

Not all regions have the same power supply.  The switchable (input voltage) PS is a PA-150B and has wall plug adapters that swap out.

These "Push" to eject adapters can support a number of different types.

The AC adapter without these is the PA-150 which I believe has a more limited input voltage range which covers the US and other like regions.

BTW: I'm not addressing if this is a good or bad feature - just trying to clear up any thoughts that these are broken or not official supplies.

I think there are worse and better ways to implement this.   If it's not very rugged (power supplies like this take a beating) then there's a good argument that the design isn't sufficient for road use.  Low voltage regions that accept the US style have it made without a piece that comes out.  This button thing looks like it could be prone to breaking or just not clicking well.  I haven't used one of these in person.   

Your story is a good one to voice to the R&D folks at yamahasynth.ideascale.com lobbying for a more robust version of the PA150B.

The parts department (YMMV) may send you a new power supply if you talk to them about the piece coming out "on its own" or somehow not staying in reliably.