Your plant is falling over because it does not have the proper environment. Indoors, the plant lacks the strong sunlight and wind it would have outside. Your pomegranate is falling over because it is reaching for the sun, it needs more light, so it continues to grow. This growth is lengthy, weak growth because the plant is not conditioned by the wind. Wind makes the plants stronger, similar to humans weight lifting.

It's better to prevent weak growth by provided adequate light and a small fan to simulate wind. However, if your plants are already leggy, you could stack the plant, increase lighting/ Air circulation. It's important to remember, you need adequate lighting/air, you could stake that plant everyday and it'll still grow tall and weak without proper sun and air circulation.

We have a section of yard devoted to native plants that grew on the tallgrass prairie that once dominated much of the midwest USA. Certain plants get tall and leggy, and tend to flop over, much like your pomegranate. It could be that they need to be surrounded by other tall plants, all competing for space, and all supporting each other. Sometimes I have to tie them up, or used some sort of support, to keep everybody upright.

That plant is leaning toward a source of light. You can rotate the pot to induce the plant to grow up straighter and continue growing straighter, or you can provide artificial light that is stronger then the sunlight coming through that window.

Here is a link that might be useful: plants and light