Here is a half-baked, preliminary thought for how "negative fading" can possibly take place. In several materials, there is an effect of "non-monotonic dose dependence". This means that up to a certain dose, the TL increases with the dose and at higher doses, the TL intensity decreases with the dose. A possible theoretical explanation has been given using numerical simulation by:

http://www.tau.ac.il/~chenr/Pubs/rpd_nonmon_tl.pdf

It is possible that negative fading can be considered as an effect opposite to dose dependence at high doses so that the thermal loss of trapped carriers may cause an increase in the emitted TL. Of course, this is merely a questionable hand-waving argument. Following appropriate simulations (or theoretical considerations) it may or may not turn out to be valid.

Nothing could be said about the results without knowing background radiation level, whether the sample was stored in dark or in room light, the type of impurity doped, whether the samples were normalized for their masses and whether heating rates were the same.

 Even if we say that different kinds of defects have been produced and some of them tunnel, the fading would occur due to recombinations. In the figure there is only one data point in the high dose range, so unless the results are checked for more data points not much could be inferred. 

These are interesting results. Generally dose build up (due to defect conversion/diffusion which is observed in LiF based samples) self irradiation (say K-40 based samples etc.) and natural background radiation tend to increase the signal whereas fading tend to decrease the signal. In view of above it seems that in the question posed by S Jafari, there is net increase in signal. The reasons can be as cited by Dr. Sharma, Prof. Chen and Prof. Sahare.

However, it must be noted that it is important to check following properties of the Glow curve under investigation:

1. Linearity range of that glow curve and history of samples  (as told by Prof Chen)

2.  Contribution of background radiation over two years when compared to freshly annealed and then irradiated samples (as told by Prof. Sahare).

3. In Fading study, (Plot the TL signal with respect to time/number of days) and Control samples (un-irradiated samples can be kept) are important for any un- usual change. 

If the material consists Potassium based host lattice, the signal may increase;; or sample has supra linearity in above dose range ;; or improper annealing if deep traps are saturated (sensitization)  or ;; there is some defect rearrangement/diffusion (as suggested by Prof. Sharma);; These may cause above mentioned effect..  I hope above points will help you.

If you could tell in detail about your exp, more explanations will emerge.

Similar effect of dose build-up has been observed in Radiophoto luminescent glass dosimeters. But, the latent period of build-up is immediately after exposure and one may have to wait for a week to have complete build-up. The effect has been attributed to the migration of charges to the luminescent centres. Perhaps a similar mechanism occurs in TLD at a later stage. 

I have also observed a significant increase of high-temperature TL signal (peak 'B') in LiF:Mg,Cu,P after 3, 5 and 8 years after irradiation with gamma (Co-60) doses in kGy region.

It is good that unlike Shakardokht Jafari, Barbara Obryk at least disclosed that the samples she used was LiF:Mg,Cu,P. But it still not sufficient to understand the phenomenon or as Prof. R. Chen says "half-backed preliminary thoughts". We have shown that in LiF:Cu nanophosphor, it is the impurity responsible for losing its reusability when it is heated above 523 K due to its redox reactions (M. Singh and P. D. Sahare, Redox reactions in Cu-activated nanocrystalline LiF TLD phosphor, NIM B, 289 (2012) 59–67, http://dx.doi.org/10.1016/j.nimb.2012.08.003) and it may also be true and occurring in LiF:Mg,Cu,P. It may also be possible during storage such kind of reactions taking place with a slow rate and such charge transfer could generate new traps/luminescence centers (P. D. Sahare, M. Singh and Pratik Kumar, Synthesis and TL Characteristics of MgB4O7: Mn,Tb Phosphor, J. Lum. 2014, in press) responsible for increase in TL or if the sample gets exposed to sun light/room light such kind of thing could occur which may increase/decrease TL. It could be basically due to migration of charges and redox reactions. 

Could this also be a property of the gain setting on the reader?  If the PMTs are saturated for the first several readings, perhaps that is causing a faulty reader response.  Just a wild guess.

I do not agree with Dr. Potter's comments. Usually, the optical window before the detector (PMT) is large enough and the readings/estimates are consistent. Also PMTs do not get saturated on repeated readings. Dr. Jafari could only tell about the faulty reader. But the possibilities are very less. Needs to probe more for finding reasons.

From my TL readout experience with a few readers of different producers with different PMTs and filtering used the suggestion by Dr. Potter is rather excluded. We are able to control/deal with PMT work. So I do agree with Prof. Sahare about this.

Our TLD reader has a Carbon-14 source for the consistency check of PMT so I can assure that reader is not faulty.

I would like to take this opportunity and thank all friends who answered my question. It is really appreciated!

Looking forward to receive more ideas.