Could the IRS argue that the 50 shares I did not sell constitutes a purchase within 30 days of the sale, and therefore consider my loss a wash sale and prevent me from deducting it?
Yes. See the Publication 550:
A wash sale occurs when you sell or trade stock or securities at a loss and within 30 days before or after the sale you:
Buy substantially identical stock or securities, ...
So you bought the 100 shares on July 1st and sold 50 of them on July 15th - you end up with a wash sale and the basis of the remaining 50 will be adjusted for the loss.
The difference from the original question you linked to was that there were no shares remaining in that scenario. There, the OP sold all the shares, and didn't repurchase. This is not the same in your scenario.
There's some confusion in the comments about the concept of "replacement shares". Note that this concept is not mentioned in the text I quoted from the Publication. It's a term used loosely to explain what a wash sale is, but the "replacement" doesn't actually need to be actual physical replacement. If you want to go into more details - feel free to read through 26 CFR 1.1091-1:
(a) A taxpayer cannot deduct any loss claimed to have been sustained from the sale or other disposition of stock or securities if, within a period beginning 30 days before the date of such sale or disposition and ending 30 days after such date (referred to in this section as the 61-day period), he has acquired (by purchase or by an exchange upon which the entire amount of gain or loss was recognized by law), or has entered into a contract or option so to acquire, substantially identical stock or securities.
There's no mentioning of "replacement" or exclusion of the initial purchase in this text.