Author events are huge opportunities to promote your bookstore. They raise customer awareness and create a sense of community between you, your bookstore, your customers, and authors. You are likely to sell more books, signed or not.
It seems that a rule of thumb among bargain buyers at bookstores, probably at the behest of the event coordinators and trade buyers, is to avoid displaying bargain books by authors who are doing book signings with them at any time in the foreseeable future, near or distant.
I get it. You never know if your author is going to be one of the few with an irrational fear of bargain. They probably are not, but the risk doesn't seem worth it. I would probably feel the same way. If you bring in a stack of their books, even a few months ahead of the event, and they sell out quickly and are forgotten, they show up in the hands of the customers waiting in line to buy the new title, in hopes that they can get this one signed too. Or the bargain book is the only one they want signed. Yikes.
Many, if not most, authors understand the effect bargain books have on their sales, which is to say, they grow them. Readers who had not tried them before buy one of their books off the bargain table on impulse and become fans for life. They buy the author's next book as soon as it comes out. But one of your responsibilities as event coordinator is to make sure your authors are as comfortable as possible coming into your bookstore and even asking them about this might seem a bit too awkward.
Booksellers would rather have the sale than know their customer is buying a "used" copy on the internet for "pennies," even though the bargain book still costs less because there are no shipping charges, and it usually costs less than the e-version as well. Bargain books are another way to ensure that the connection between your bookstore, the author, and your customer remains intact.
If this bargain book avoidance is something you practice, I would recommend that you moderate it a bit and buy the bargain books, just don't display them during the three or four weeks before the author's event. Wait a bit after the event, maybe until the next weekend, then do a display on your bargain tables. Customer interest in this author will be at its peak and you will generate some new readers for their works.