OnPressed-->prop_dynamic-->SetAnimation-->start delay: 0
OnPressed--!self-->lock delay: 0
OnPressed-->prop_dynamic-->SetAnimation-->idle delay: 10
OnPressed--!self-->unlock delay: 10

However, the prop_dynamic doesn't animate when I press the button the second time after 10 seconds.

Anybody knows why?

Brainstone, this is what VDC specifically says about the func_button:
(https://developer.valvesoftware.com/wiki/Func_button)

"Bug: Do not lock while pressed; it will not return when unlocked."

Could it simply be a bug?

What exactly are you setting this button for exactly? Anyway, I guess what you want is to prevent the interruption of the prop_dynamic animation, right? Well, 3 things:

1. Maybe the fact that the button itself is the one that fires its own outputs is causing a conflict... you could try introducing a couple of logic_relays mediating there, and use any settings as the following ones for example:

Func_button (set "Delay before Reset" to 10 secs):
OnPressed > Relay_1 > Trigger
OnOut > Relay_2 > Trigger

Relay_1:
OnTrigger > Relay_2 > CancelPending / delay 0.00
OnTrigger > [prop_dynamic_name] > SetAnimation > [whatever] / delay 0.20

Relay_2:
OnTrigger > Relay_1 > CancelPending / delay 0.00
OnTrigger > [prop_dynamic_name] > SetAnimation > [idle?] / delay 0.20

1. Also you can set the delay before reset to -1 (so it stays), and use an external logic_timer for the reset instead. Then, stop the logic_timer when you want the button to be unlock again.

2. Maybe you are using a bad output for the prop_dynamic: "Start"?? isn't it "Open" or "Close" or "whatever" instead?