I would approach this problem by trying to determine where the failure in the system is. It is easier to find that failure if the normal operation of the system is understood.
There are (at least) five parts to the system.
1) The flipper cabinet buttons (leaf or opt).
2) The drive transistors for the power stroke and the hold stroke (fliptronic board).
3) The solenoid that creates the magnetic field corresponding to the power stroke and the hold stroke (FL-15411).
4) The wiring connecting all the components (wires and ribbon cable).
5) The (CPU) program logic connecting the inputs (switches) to the outputs (drive transistors).
Each of these parts can be tested to determine the source of the problem.
1) Enter tests and select T1 (switch edges). Press the flipper cabinet buttons and ensure the program logic detects the switch closures.
2) Enter tests and select T12 (flippers). Make sure the test is either RUNNING or REPEAT (if repeat advance manually).
3) Measure resistance across the solenoid lugs to ensure that the resistance is in the appropriate range. BSD should be FL-15411. The power wiring should have a resistance around 4 Ohms. The hold wiring should have a resistance around the 100+ (from memory) Ohm range.
4) Continuity between the appropriate points should be measured to check wiring.
5) This is unlikely because if this were the problem you'd have bigger issues than you're reporting.
Based on your description of the power stroke functioning but the hold stroke not functioning it's more than likely to be electrical. Check the drive transistor (TIP102) on the Fliptronic board. Test T12 should also confirm this.
Notice that I did NOT mention the EOS. It has nothing to do with powering the hold stroke. The EOS is used to re-enable the power stroke if necessary.