If it is lab research; All the materials should be stored under Argon/Nitrogen atmosphere to protect them from the moisture/water.  

If it is bulk production; It should be stored very well ventilated store at room temperature and very well sealed drum not IBC but always away from moisture/water.

Please, give some more details on the composition and conditions of synthesis as there is a difference if you use aliphatic or aromatic compounds, solvents, catalysts etc. The reason maybe a crosslinking via biuret or allophanat linkages or simply a trimerisation of residual isocyanate groups but without further information this is a guessing game.

Thanks dear Metin and dear Gerhard

It based on TDI with DBTDL as catalyst and the solvent is toluene 

TDI (2,4 or 2,6 or mixture of isomers?) is one of the most susceptible isocyanates for sidee reactions. Toluene is difficult to receive as anhydrous solvent. BTL should not be the catalyst of choice. Thus, check for the water content of toluene which should be lower than 0.01 %,. check for the purity of the TDI (is this a water clear liquid?), change the catalyst to either triethylamine at low concentration or to tin dioctoate the same. Try to get an FTIR spectrum just after sysnthesis and after three days. Check the bands at 1709, 1420, and 1685 cm-1. If there are shoulders you get a proof of side reactions as the reason of your crosslinking phenomenon.

I think for store the PU-resin at low temperature, and  in  the darkness.

Avoid light.

as previous responders mentioned : exclude moisture, oxygen, (UV) light, and keep cold to reduce reaction rate.

I am not specialized in polyurethanes but I shared a laboratory with a classmate who did PhD research in polyurethanes. Very often, we discussed his observations & his work. The prepared PU is among 3 possibilities: both terminals are OH groups, both terminals are isocyanate groups, or one terminal is hydroxyl & the other terminal is isocyanate. To store an unfinished PU resin, just  keep it away from moisture, wet air, and UV light.

First keep it in dark place and exclude moisture.

exclude moisture, oxygen, (UV) light, and keep cold to reduce reaction rate.Also use dried solvent.lower amount of catalyst depends on formulation and condition of your samples.

Check the catalyst and reaction conditions for side reactions. If there is no change, add 0.1 % of toluene sulfonic acid methyl ester

check your polyol functionality first, the temperature you work is another important issues and working between 70-75 is better, and finally one of the reasons could be the access of isocyanate which trigger side reactions by the time and crosslinking is one of them, you can check hydroxyl and NCO content

If you want to have a long life, you should add polyurethane inhibitors to the reaction. For example; Such as SiCl4, BCI3, AlCl3, TiCl4.

In addition to these, the most commonly used polyurethane inhibitors are known as benzoyl chloride and toluene sulfonic acid methyl ester. Use between 0.1-0.3%.