Conjugation increases the allylic strain because it forces substituents into a configuration that causes their atoms to be in closer proximity, increasing the strength of repulsive Van der Waals forces.  This situation occurs most noticeably when carboxylic acid or ketone is involved as a substituent of the allylic group.  Resonance effect on the carboxylic group shifts the CO double bond to a hydroxy group.  The carboxylic group will thus function as a hydroxyl group that will cause a large allylic strain to form and cancel the stabilization effects of the extended conjugation.  This is very common in enolization reactions and can be viewed in the figure below under "Acidic Conditions."
In situations where the molecule can either be in a conjugated system or avoid allylic strain, it has been shown that the molecule's major form will be the one that avoids strain.  This has been found via the cyclization in the figure below. Under treatment of perchloric acid, molecule A cyclizes into the conjugated system show in molecule B.  However, the molecule will rearrange (due to allylic strain) into molecule C, causing molecule C to be the major species. Thus, the magnitude of destabilization via the allylic strain outweighs the stabilization caused by the conjugated system.