I have found a possible reason with my partners. We are analyzing LEDs, not circuit problems. The LED is determined to be bad.
The welded silver paste cracked
A "possible reason"? If you want to "analyze" LEDs, you should purchase bare (un-packaged) dies and probe these with micro-adjustable wire test leads. No need to worry about cracking "welded silver paste" (or whatever) if you analyze the LEDs in that manner.
All the "big boy" semiconductor manufacturers do it this way, sometimes with hundreds of individual test leads probing a die simultaneously, depending on die complexity. The companies that make the micro-adjustable lead fixtures and wire test lead probes go to a lot of trouble to electrically characterize their probes, which allows the effect of probe lead resistance, inductance, and parasitic capacitance to be taken into account when reviewing the test results.
All this is usually done in a Class 1 clean-room environment, by workers encased in bunny suits with filtered breathing-air supplies. Of course you can do it on the cheap by just washing your hands, putting on a clean set of blue jeans, and squeezing a packaged LED with a pair of Vice Grip pliers to "de-cap" the lens, but your test results may be variable.
LEDs appear to be mass produced by injection molding plastic around pre-assembled lead frames attached to LED dies. Perhaps you can contact one of these manufacturers to obtain the lead frames with dies attached before the plastic molding is applied.