Just some handy information I dug up. Each enemy has an escape rate which is compared against a random number that is generated when you attempt to run (between 0-255). If the number rolled is larger than the enemy's escape rate, you are blocked. Also, in the case of different enemy types, the enemy with the lower escape rate is what the random number is compared against.

Knowing these rates can be handy when trying to improve your times, that way you can know which enemies you will have to fight in order to save time, or which ones you can run away from with near certainty.

For the sake of simplicity, here is a list and the odds of being able to run from each enemy. Bosses are not included.

Fire Ant 70% Armor Ant 70% PinchAnt 60% Mosquito 60% Waspy 50% Stinger 40% Spinner 20% Vortex 30% Whirly 20% Bee 70% Buzzer 80% Insecta 70% Poisoner 70% Spitkill 60% Spitfang 60% HitTail 20% Center 10% Scaly 10% Froggy 8% Toader 20% Squat 20% Carrier 30% Mushroom 30% HeadRot 30% Whistle 70% Informer 70% Tracer 100% Locust 40% Locusta 30% Fanbite 20% Amoeba 60% Jelly 70% Slugmess 60% Polezi 70% Poleziax 80% Poleziss 100% Leecher 70% Fang 80% Python 60% Pulser 10% Blaster 20% Blastoid 20% RotWood 70% Blockhed 80% Firia 70% Wolfang 80% Burnwolf 80% Flarewolf 80% Pughit 80% PugBrat 90% PugKill 90% Wireface 40% Wirehead 40% Podhead 40% Terakite 70% Reptile 80% KiteDrgn 80% FireEye 50% Glowstik 60% Forest 30% Catman 60% Catfang 50% Cateye 40% Mechoman 90% Sonomech 80% Attmech 90% Mazgamma 80% Firgamma 70% Kilgamma 80% Metalman 80% Twigman 70% Twigtall 80% Cooley61 60% Monster 40% Lrgminer 30% Eyesore 50% Hvysolid 40% GunBust 50% Trcrbase 10% Specter 20% Van 10% Aerotank 30% Orangah 80% Orangoo 80% Ohx 80% Mastodon 80% Eletusk 70% Elephant 70% DezoOwl 70% Skytiara 80% Owltalon 50% Rabbit 40% Rabitta 40% Rabitgut 40% Wrestler 80% Sakoff 80% Mesoman 20% Lung 10% Glosword 20% Desrona 70% Darkside 10% MrDeath 10% Shadow 10% Mystcape 30% Illusnst 70% Imagiomg 30% ArchDrgn 50% Frdragon 40% Mxdragon 60% Firefall 10% Vorcano 20% Kinglava 40% Wizard 30% Capeone 40% Fiend 30%