How to Prevent Breast Implants from Bottoming Out?

The only thing you can do to avoid bottoming out is probably for your breast aug to be done by the most qualified individual in your market ... an ABPS Board Certified Plastic Surgeon.
Outside of that, there's no bra that'll stop the drop if the job was poorly done. If the implant is really, really big and you're really, really tiny, the chances of bottoming out are greater. It's not clear to me if you've had surgery yet or not. If you've not, then the only indicator that I've seen in patients preop is if they have stretchmarks and signs of very lax tissues within their breasts, the chance of bottoming out is higher so the surgery needs to be tailored for your body to avoid this problem by limiting the release of tissues inferiorly.
If you've already had the procedure and they're starting to bottom out, then you may be dealing with the inevitable, but there's no harm in using a good supportive bra all the time to stretch it out as long as you can. For this there are new products available but that's a whole other topic.

Large Implants due to their weight, gravity, thinning of tissues, chronically not wearing a bra, loss of elasticity and other factors may cause continued stretching so that your breast implant is no longer supported in its ideal position. This results in the progressive lowering of the inferior breast crease (inframammary fold). When the implant moves South to an undesired inferior position it results in the loss of volume and flattening of the upper pole of the breast, too much volume at the lower pole, increasing the distance from the fold to the nipple and finally the nipple position being abnormally high ( pointing up) and not centered. Similarly, the pocket can also stretch to the side (lateral) so that when lying down your implants fall towards your arm pits or sides, causing the “Side Boobs” appearance.Bottoming out and Side Boobs Contributing Factors:Larger/Heavier ImplantsImplants placed above the pectoralis muscleChronically not wearing a bra when uprightOver dissection of the Implant PocketSmooth ImplantsLarge swings of weight including pregnancySkin and soft tissue laxity, loss of elasticity

Well, first and foremost, the surgeon should use breast implants that are of an appropriate size and shape for a patients starting point.  Overly large implants frequently over time will stretch out the skin and the soft tissue of the lower pole allowing the implant to descend and create that bottomed out appearance. Some patients need to have their inframammary fold lowered in order to achieve an aesthetically ideal implant position, and that is another setting that creates some risk of, over time, a bottomed out appearance. There are things that can be done, however, in the setting of intentional lowering of the inframammary fold to prevent that outcome. One important thing to do is to use an inframammary fold incision, and at the end of the procedure, after the implants are placed an anchoring suture can be placed to secure the deep connective tissue of the skin to the connective tissue of the chest wall. This creates at least temporary barrier as the implant is healing reducing the likelihood of the implant settling over time. Another important thing to consider is implant selection when you are lowering the inframammary fold. Currently implants are available with a high degree of capsular adherence to the implant surface. If the capsule that your body forms around the implant becomes adherent to the implant surface, then this will help it to remain positionally stable over time. 

“bottoming out”  is the term used to describe the condition which occurs when the breast tends to look as if it has descended on the chest wall after previous surgery,  whether the surgery involved implants, a lift, or a reduction.  In the case of “bottomed out” implants,  sutures can often be placed in the lower pole of the breast to re-elevate the breast on the chest wall.  This is called a capsullorraphy and can achieve excellent tresults in the correction of “bottomed-out implants.  the risk of bottoming out can be lessened by correct pocket dissection

Bottoming out cannot be completely prevented.  Most times it happens early on because the fold was violated.

Bottoming out is a problem sometimes seen in patients who receive breast implants that are too large for their breast and these women often have excess breast skin. Selecting the correct size, shape, and position of the implant can help prevent this problem.

First and foremost you should chose an experienced board-certified plastic surgeon to care for you.
Your plastic surgeon will examine you and help you make a determination as to what size/style/type of implant will suit you best for your tissues and what you are trying to achieve.
Implants can thin the tissues of the lower breasts so the larger the size the chose, the higher the risk of this is.
Dr Edwards

I am not completely sure what you mean when you say "bottom out". If you mean sag, yes they can, just like our natural breasts do. This tendency to sag is affected the size of the implant, the natural genetic tendency we have for either tight or loose skin and our natural aging process. By selecting smaller size implants, you will do less damage to your tissues. Wearing a bra is extremely helpful for everyone. It helps prevent the breast skin and tissues from stretching out.

There is confusion over the term "bottoming out" as it may refer to inframammary fold overdissection or overstretching of the lower pole of the breast. Prevention or correction depends upon whether surgery is primary or revision and skin quality. Some complicated revisions may need Strattice (pig dermis) or human equivalent. We use bra support after these revisions to aid healing. I am not sure whether wearing a bra past the initial healing period really prevents any of these issues.