Besides bad luck, if the pet is not around level 50 then it will not get portals to go to higher levels.The higher level the pet it the further it can go.
I think it is connected to the fact that when you have lower level pet the map is smaller and you have less possibility to spawn a portal to next level.
When I was trying for the Etelia I actually used pet from lev 1 (and it levelled quickly with a few energy drings and many portal cells) and the difference between him not going further at low levels and not going further at his lev50 is not a big one.
From my experience I verry often go to lev 4-5, but to go further is about 1/3 explores. I actually seldomly find lykos eggs though. And they are usually after the verry good guardians - even my good pet that can take me to lev 11-13 sometimes loses to these lykos-egg-guardians at lev 4. Interesting fact is that I found lykos eggs only at levs 3-5, mostly at lev4. But as I say I only found a few of these eggs, so I may not have enough experience. But if you are hunting for lykos eggs try going to at least lev 5 and fight with all the guardians - not make a rooky mistake I first did - that I skipped problematic guardians unless I couldnt find a portal to next level.
I will buy/swap for GENETICIST INVITES and TRAINER INVITES!!!
Also looking for Magical Fruits (Glowshroom, Dragon Maple, Nutpea, Cactus MelonHeart Fruit, Bambo Berries) -> offering 7ooo silver for each.