Size:
Always use the size eyes called for in pattern or appropriate size for gauge, if you are using a bulkier yarn (thinner yarn) than the pattern calls for you will want to increase (decrease) the size of your safety eyes to keep the proportions correct.
Security:
I have never had any of my eyes come loose and fall out or have the backs come off once applied properly but I have had the top portion of the eye break at the post (Note: it was a bad batch and once I threw them away, I have not experienced this again). I suggest giving the head of the eye a few good tugs just to be sure it's not faulty.
Other ways you can add extra security is to...
Add a spot of glue on the post before adding the backs.
Melt the tips of the post after adding the backs.
Placement:
When applying safety eyes it is always important to make sure placement is precisely where you want it BEFORE attaching the backs. Also if you are using felt, yarn or floss behind the eyes, be sure to apply those BEFORE attaching the backs. Once those backs have been put on, they are permanent.
Purchase:
All eyes used in Southern Gal's Crochet patterns were purchased at crscrafts.