I tried to reproduce the problem in a small project but I was unable to as it works as expected. The global flow of the B4XPages app is :
Starter service -> Call app_dm.InitApplication -> MyClass.Initialize which init other child classes that are using app_const in their initialization section.
Here is a small project, but no issue.
The real app(s) still have the problem.
I can use workarounds like changing the data module to a singleton class and call initialize or get ride of the const and use var instead, but I wish I had been able to find the source of this problem...
Here is the small project, just showing the global flow fo calls