I often have ladies ask me the same question and during my days working on beauty counters customers would often ask for mascara that doesn't smudge.
My first question to you would be to look at what you are using to remove your eye makeup. Often if using an oil based eye makeup remover or cleanser a small amount of oil residue may remain on the lashes the next day. If you apply your mascara or liner on this residue it will simply slide off.
Another cause can be using too much eye cream. As eye cream warms up on the skin it may move towards your lashes again causing mascara to move and deposit.
My recommendation would be to thoroughly cleanse the eye area with a water based remover and if you are using a cleansing oil or balm then remove thoroughly with a wash cloth.
Regarding eye cream you only need a tiny amount (around the size of a grain of rice) and divide between both eyes. Pat this onto the orbital bone where the cheek and eye meet.
Great eye makeup removers include Bioderma Sensibo H20 Micelle solution which will remove all eye makeup except long wear. If wearing long wear then you will need an oil based remover such as Bobbi Brown Instant Long Wear Make Up Remover.
Another great tip if you are prone to oily eyelids is to introduce an eye lid primer into your routine - one of my favourites is Smashbox Photo Finish Lid Primer. This will ensure that your eyelids stay matt and you can wear either on its own or under eyeshadow.
Good bye to panda eyes!