As Rohat Kılıç says, your problem is the internal resistance of the batteries.
A simple regulator won't prevent the battery voltage from dropping. If you use a boost/buck type regulator, it could hold the voltage to your device steady - but it would have to be capable of providing enough current for your device and the motor.
The thing is, that voltage drop is trying to tell you something: your load is too heavy for your batteries.
Because of this, your batteries will not operate your device for very long.
You need larger batteries.
1.5V batteries come in various sizes, from AAA to D. Try moving a size or two up. If you are using AA size batteries, move up to size C or D.
The larger size batteries have more capacity (they provide power for a longer time) and their internal resistance is lower (you can draw more current but have less of a voltage drop.)
If that doesn't help, then you can try a couple of other things:
- Put batteries in parallel. This will increase the current they can supply and reduce the resistance. The battery capacity also adds. Use only batteries of the same type.
- Use a larger battery. Say, a 6 V sealed lead acid battery or a 6V lantern battery.
Ideally, you would measure the current that the motor or solenoid needs to operate. You could then look up the datasheets for various batteries, and look at the discharge curves for that current.
That would show you the voltage drop and the expected operating time before you buy a set of batteries - it would save you time experimenting, since you can skip trying out batteries that have no chance.
To be clear, the "internal resistance" isn't some separate part installed in the battery by the manufacturer in order to force you to buy a bigger (more expensive) battery
It is a consequence of the size of the battery.
A small battery has less volume for the reactive chemicals, so it has less capacity to deliver current. Kind of like a small bottle has less volume than a larger bottle and so holds less liquid.
A small battery also has less area for the plates of the battery. More area gives a lower resistance.
Physics and chemistry limit the capacity and internal resistance of the battery.