Here are some things that have to be looked at, with the assumption that this is a heat seal and not glue, that the heat seal material is some kind of plastic (ie.: polyethylene or PVC), and also assuming that the paper is curling at the edges:

• Does the paper cover the entire surface - is it sealed to the entire surface?
• Has the seal strength been measured on an Instron or similar equipment?
• It is likely that the coefficient of expansion of the material is allowing the rigid surface to expand during storage, causing the material to release in orderto relieve the stress at the seal.
• The interface between the coated paper and rigid surface must be understood.
• The bonding material used to seal the material would need to have similar properties (coefficient of expansion), though this may not help.

Some follow-up information would be helpful to provide a more detailed answer. For example,

• Heat seal material?
• Is this a chemical seal activated by heat or moisture?
• Is this strictly an adhesive - how is it activated?
• What size rigid material? Flat? Solid? Or does it have cavities that are being covered?