E.g. - i.e. (punctuation)
The eminent scholar David Crystal in his The Stories of English (2005) frequently writes e.g.,, with both letters followed by a full stop (as they are abbreviations), and the whole group followed by a comma -- as if it were the phrase for example, which is usually (but not always) followed by a comma. His usage strikes me as logical and correct - even hyper-correct - but I do not use it. Such are the burdens of prejudice in terms of linguistic usages! You must make up your own mind about how you want to punctuate the abbreviation; but, whether or not you are following it with a comma (or other punctuation mark), I beg you not to let a grammar checker on a computer delete the full stop.