Upper premolar teeth gap can be maintained without worry of toothache?

Grand canyon: If a tooth is removed in the middle of an arch, the surrounding teeth tend to collapse into the space provided. Teeth in the opposing arch over-erupt into the space. This can destabilize and allow flaring of anterior teeth. Teeth out of position can "clash" and become sore, wear down, fracture. Talk to your dentist about replacement to prevent these unfortunate circumstances.

Maybe: Not really sure what you are describing? If the is a space between teeth, keep it clean with floss. If teeth are missing, again keep area clean.

Question is Vague: Not sure what you mean exactly. If you have a gap or space between your teeth, that should have no influence on whether you develop a toothache. If the teeth on either side of the gap are healthy, & you don't abuse them, they should be just like any other teeth. However, if you're missing a few teeth, then the remaining ones can have a higher functional demand placed on them, so they can get sore.

Gap not pain cause: A gap will not cause pain unless the adjacent teeth are decayed or have periodontal problems.