There are two common things that might stop you from getting your tongue pierced:

1. First, is overly prominent veins on the bottom of the tongue. Sometimes they can be avoided (so you may want to get a second opinion from an experienced piercer if you are told no), but there are rare cases where it would not be safe (i.e. you may bleed uncontrollably, potentially leading to death).
2. The second thing that can make a tongue piercing difficult to impossible is an overly prominent tongue web (that holds the tongue to the bottom of the mouth). If it is too long and tight, you won't be able to stick out your tongue, making it difficult to pierce, and, in addition, a piercing would rub on the webbing leading to discomfort.