Thanks for the question.

As you are discovering, spider mites can be very difficult to eliminate. Although so far you have done an admirable job in dealing with them, it does take patience and persistence. My best guess is that your current population of mites came from your previous lime plant that you discarded. There were probably adult mites still lurking about when you brought in the replacement plant. There are several different species of spider mites. One of the most common species that infests indoor citrus plants is the "citrus red mite" (Panonychus citri). My guess is this was the species of spider mite that infected the lime plant that you had to discard. The citrus red mite is a type of spider mite that feeds on the sap of citrus leaves, causing damage to the foliage. Infestations can lead to symptoms like stippling (tiny, yellowish or reddish spots on the leaves), leaf discoloration, and, if left untreated, reduced plant vigor and fruit production. Since this mite strongly favors citrus plants, this is probably why you don’t see it on your other plants. See:

https://ipm.ucanr.edu/PMG/GARDEN/FRUIT/PESTS/citrredmite.html - :~:text=Citrus red mite—Panonychus citri,during late winter and spring.

Spider mites have about a 25-day life cycle, adult to adult. The best way to break this cycle is to eliminate adults so they can’t mate and lay eggs. Right now in your latest lime plant, new adults are constantly arising and laying eggs. For them it’s an ongoing process. This means that daily treatments must continue for at least three weeks to kill all adults that may arise during this period of time.

As a first step, completely isolate your lime plant from all other plants ASAP. It is possible that spider mites may have laid eggs in the soil of these other plants. If so, then when these eggs hatch, you don’t want the resulting adults seeking out your lime plant.

Having done this isolation, consider the following for your latest plant:

1). Prune and remove heavily infested leaves or branches to reduce the mite population and improve air circulation. Put this plant material in a tightly sealed refrigerator bag and throw into your trash.

2). Repot (yet again!) your new lime plant using fresh potting soil. Clean the pot thoroughly with a 10% bleach solution (1 part household bleach with 9 parts of water). Thoroughly rinse the pot and let air dry. Then transplant.

3). Continue using neem oil or other appropriate miticides to treat the infestation. Follow the manufacturer's instructions carefully. In order to break their life cycle and recognizing that new adults can emerge over a period of three weeks or so, do this treatment on a daily basis for at least that long.

4). Spider mites thrive in dry conditions. Increasing humidity around your indoor citrus plants can help deter these pests. Use a humidifier that is close by the plant and/r mist the plants regularly.

I’m reasonably sure that having done these various things, you will gradually see a reduction in adult mites and/or in their webbing.

Best of luck to you. As I said, persistence and patience will be necessary. Please get back to us if you have any questions.

Glad to have helped.  Thanks for consulting our forum.