It is not quite clear from your question whether you were re-testing the same sample or another set of samples from the same film but which had been stored.  In both cases, but especially in the first case, the result would differ. In the second case, storage conditions can have a detrimental effect on tensile strength. The reduction you report is large.

I assume you have included controls before and after each set of tests to ensure the instrument is functioning in the same way.

Yes, it is possible that changes in tensile properties would occur on storage. If the films or polymers are suspectible to hydrolysis. However, with that large deviations, you may have to look at the applications and will this product serve the intended purpose, if its for packaging then, it may be a biodegradable product (disintegrate easily ).

Probably, your a very thin films are strongly affected to degradadion, particularly, to embrittlement in time, even in the absence of noticeable UV light exposition.

Then the microcracks and other structural defects "begin to work" and promote dramatic strength decreasing under tension.

And another possible factor may be connected with relaxation of stresses in extruded films during time out. 

I presume Its a commercial pure LDPE film (no LDPE/LLDPE blend). Typically, commercial LDPE resins contain both, antioxidant and UV stabilizers. Due to additives presence, LDPE is not susceptible to hydrolysis or UV degradation (presuming its stabilized).  Some one suggested micro-crack and refers to papers on blends. LDPE is a very flexible, low crystalline material that should be quite stable at normal storage conditions and will not hydrolyze either. If it were blends yes, phase segregation with time may result in degradation of tensile properties.  So, the question of phase segregation with time in this case does not sound plausible.

Now, here is the real conundrum! Seems like its a real thin LDPE film. Was this film made by down gauging? In that case due to machine direction orientation (MD) mechanical properties will be very different in MD vs. TD direction. Since, LDPE has lots of branching, tensile in TD direction will be vastly different than MD direction. So, when you tested the film, were you really careful as to maintain the same orientation (MD vs TD)? 

Another question. Due to high level of short and long chain branching in LDPE and due to quenching of film during making, you may not allow the film to attend equilibrium state of crystalline. In such a case, the quenched film at room temp. will have tendency to crystallize further. As you may know, higher the crystallinity, poorer will be the tensile strength (but will have higher modulus). So, I would suggest run DSC and/or WAXD to check the difference in level of crystallinity between fresh Vs stored LDPE film along with making sure that there was no mix up in the specimen orientation direction.direction. By the way, I presume that you were careful not to test a creased vs non-creased film as creased film will fail faster. Hope this helps.

I totally agree with Abaneshwar and Amir.

I would simply add that such small thickness may not prevent from formation of holes resulting from the frozen-in bi-axial stresses caused by drawing. The stresses cannot relax anywhere in film plane and in presence of surface irregularities  (stress concentrators)  my have caused micro-holes formation along the elapsed time.

It is possible occured on each materials. Some time the changing properties of material is depend on the environment. Generally, when keep the matrial have to conditioning on the degassing box.