How to prevent eggplant having a tough or rubbery texture

Make sure your initial cooking is reasonably fast and hot, and from there just cook it until it's soft enough for your tastes.

Many vegetables firm up when cooked at lower temperatures, especially in the presence of salt. From On Food and Cooking:

It turns out that in certain vegetables and fruits - including potatoes, sweet potatoes, beets, carrots, beans, cauliflower, tomatoes, cherries, apples - the usual softening during cooking can be reduced by a low-temperature precooking step. If preheated to 130-140F/55-60C for 20-30 minutes, these foods develop a persistent firmness that survives prolonged final cooking. ... Firm-able vegetables and fruits have an enzyme in their cell walls that becomes activated at around 50C (and inactivated above 70C), and alters the cell-wall pectins so that they're more easily cross-linked by calcium ions. At the same time, calcium ions are being released as the cell contents leak through damaged membranes, and they cross-link the pectin so that it will be much more resistant to removal or breakdown at boiling temperatures.

Eggplant isn't on that list, but I believe the enzyme in question is pectinesterase and is present to some degree in many vegetables, and I've had eggplant that stayed fairly tough through longer cooking, so I suspect it's a possibility here.

You need a minimum cooking time and water for it to be cooked thoroughly. You mentioned that once they turned out tough and chewy: then they were not cooked fully through.

Vegetables are not like meat, which turn rubbery when overcooked. They turn soft rather.

Watch out for the opposite as well: Eggplants when cooked for a long time may turn mushy.
Cut them and keep them immersed in cool water prior to cooking to avoid discoloring. Then start by cooking with minimal water. Cover and cook. Keep stirring in between. Cut with a spoon to check if it is cooked. The spoon should softly pass through the piece.
You can also taste it: if you achieve the melt in your mouth (not mushy though) stop your cooking process.

I cook with eggplant very often. Nearly always I microwave them first, either whole or in pieces, for up to ten minutes at about 750w. This leaves them soft and less bitter, and ready for browning in the frying pan or oven.

I find for eggplant parm, slicing thin is the key. If too thick can be tough and rubbery...awful and inedible.

I cooked two eggplants earlier today, both very large, in halfs. The two larger slices came out rubbery and inedible, and the other two, (smaller) were cooked through and through and came out soft like whip cream, and delicious. So thickness made all the difference here because all the other factors - temperature, salt, humidity etc., were the same. The larger half of each eggplant came out bad and the other half bad. From now on I'll be cooking medium or small size eggplants see what happens...