I am very pleased at the amount of detail you have shared with us, I have experienced similar problems before but the cause was different in every instance.
1. Have you removed trial weights when putting in correction weights and is your system doing correction calculations based on removing or leaving on trial weitghts?
2. Is your tacho firmly achored on the magnetic base or whatever mounting method you use and your 0-degrees blade or mark inline with a reflector tape and your tacho for correct phase reading?Is your accelerometer firm and in correct orientation?
3. Are you using positions or continuous angle divisions? How many blades are on the fan? What is the RPM of the fan?
4. Have you inspected the structure for cracks?(this tend to affect your 1xTS and fools the program when doing calculations)
5. Are you balancing at operating speed?
6. Now...from the data you sent, what i do differently is, after a reference run, i look at the 1xTS amplitude magnitute and phase value of each plane, for 600-1500 RPM machines i add 90 degrees and 45 degrees on 1500 - 3000 RPM on the reference phase in a direction of rotation, that will be the location for my trial weight, the magnitute of the weitgh will be determined by the shaft & bearing sizes, RPM, the reference run 1xTS amplitude as we as the fan rotor diameter, take your trial run and make sure the phase shift results while capturing data is 30% or more, this is neccessary for the software to compute a more reliable correction solution.
7. Make sure whether your software needs you to remove or add on trial weight when installing the correction weights and do as required by it.
> What i noticed from the data you sent, your phase shift values after trial run are not ideal, well im no expert, but so far it works for me if the shift is more than 30% and does not work if it is less than that. Another thing is, your reference run phase and a correction phase is almost similar, that is why your balance is unsuccesful, there must be a mistake you made with phase readings or setup of your apparatus or in the software, look at your tacho location setup and accelerometer oriantation setups as well as your direction of rotation setup, and make sure you balance at operating speed.
> I highly doubt the balance is affected by mechanical faults...Good Luck.