Got my TR to 18 (12ftr6monk) last night and pulled his holy burst and shocking burst rings out of the bank, noticed missing damage numbers on some wraps while running around in the vale. Played around on the training dummy for a while tonight and have kind of narrowed the problem down to wraps with lacerating on them, Ivy wraps, and his Alchemical's.
Basically this is what happens: With a level 12 mabar wraps equipped, damage from both rings works just fine. When I then equip a +5 Holy Festival Icy burst of lacerating wraps, I lose the holy from the wraps themselves. The holy burst works fine (seeing two sets of holy damage on crits), but no straight holy damage from the wraps. Shock damage from ring still works fine.
Now, scenario two: Those same +5 Holy/icy/lacerating wraps equipped, if I switched to his tier2 double air alchemical wraps, I lose the holy burst from the ring altogether (note that I also lose the shocking burst ring, but its always been like that - same burst effects on wraps and ring have never stacked). Only damage numbers that show are base and the shocking burst from the wraps. If I switch to those mabar wraps again, both rings work fine. From mabar back to double air alchemical, the holy damage from ring is suddenly there.
Scenario three: The alchemical wraps equipped, I switch back to the +5 holy/icy/lacerating, and now suddenly the shocking burst damage is gone. By switching to any other non-lacerating wraps and back, shocking burst returns.
Ivy wraps seem to be losing the effects in the same way. Have a pair of heroic norm, have them equipped and I get both ring's damage. Switch from Ivy to alchemical and back, I lose the shocking burst. Switch to the +5 holy/icy/lacerating and back, now both ring's damage is gone except on crit, where holy damage shows up. Switch to any other handwrap that isn't alchemical or lacerating, and back to Ivy, everything is reset and works fine.
For reference, I also tested a pair of +1 holy/icy/stun 10 wraps and everything was fine. Got two sets of holy damage numbers (3 on crit), shock damage was there and no amount of switching back and forth changed that. The problems seem to be concentrated on the interactions between a holy of lacerating wraps, double air alchemical wraps, and the Ivy wraps.
The TLDR is this: Switching between a holy of lacerating, double air alchemical, and Ivy wraps causes the damage from the burst rings to disappear. You can equip any other (non-lacerating) wrap to reset this. The exception is that no amount of switching around will get a holy burst ring and the holy on holy/lacerating to stack.