When I try to store chseled blocks in the clipboard with the "/c&b.exportmodel" command the items are stored and the file "chiselsandbits_clipboard.cfg" gets some content. But after closing Minecraft and start it again the file does not seem to be recognized and the clipboard is empty again.

MC Version: 1.12.2
C&B Version: 14.30
Do You have Optifine: OptiFine_1.12.2_HD_U_E3.jar
many other mods

but I also tested it with MC vanilla + jei + chiselandbits only.

You seem to be confused regarding the word clipboard usage in the mod.

/c&b.exportmodel stores the JSON ( raw mincraft model data ) to the system clipboard, this part of windows/linux whatever OS your using. This feature is for resource pack and mod developers.

The creative clipboard, as provided by C&B is not related in anyway. To add a block to the creative clipboard there is a hotkey you can assign. It also by default adds blocks you break to it.

You'll want to use the keyboard shortcut to add a block your looking at too the clipboard, so you can then pull it back out and place it in the world.

OK, thanks for clarifying the difference.
Anyway, the block was in the Chisel and Bits Clipboard tab in the inventory (since I was playin around and building and destroying the blocks), but after a Minecraft restart it was gone.

That was very quick, thank you!

Will be fixed in C&B 14.31