1790112 - SYB: SYSTEM_CLASSCONSTRUCTOR_FAILED dump in monitoring transactions

Monitoring transactions like DB02, DB12, DB13, .. and RZ70 fail with the following short dump:

Category                        ABAP Programming Error
Runtime Errors               SYSTEM_CLASSCONSTRUCTOR_FAILED
ABAP Program                CX_DBA_ROOT===================CP
Application Component   BC-DB-DB6

[...]

The current ABAP program "CX_DBA_ROOT===================CP" had to be terminated because it has come across a statement that unfortunately cannot be executed.       

[...]

While the class constructor of class "\CLASS=CL_DB6_SYS" was running, a condition occurred under which the class constructor should be exited prematurely.
This is illegal, because the class turns out inconsistently.

[...]

System environment      
    SAP Release..... 731
    SAP Basis Level. 0000

[...]

|   85|*         not batch, not in framework:  
|   86|          message e066(db6pm).          
|   87|        endif.                          
|>>>>>|      else.                             
|   89|*       batch:                          
|   90|        message s066(db6pm).            
|   91|      endif.                            
|   92|    when others.

Netweaver-based SAP systems with an ABAP stack running on Sybase ASE
SAP Basis Release is 7.31

DBACOCKPIT, RZ70 , KBA , BC-DB-SYB , Business Suite on Adaptive Server Enterprise , Problem