Sequence of events:
- Enterprise detects Constellation at outer edge of system and gets there in a minute or so (approx the 3rd planet location). Probably with warp drive ala "Breads and Circuses".
DM enters detection range of the Enterprise and forces her to leave the Constellation. The Enterprise circles around the Constellation maintaining transporter range.
- Enterprise lowers shields and is hit by the DM, losing communications and transporters.
- Enterprise outruns the DM. DM turns away to next star system.
- Enterprise turns back to attack instead of circling around and away from DM to pick up Kirk.
- Constellation regains impulse power and phaser capability.
- Enterprise loses warp drive and is caught in DM's tractor beam about to be pulled in.
- Constellation fires phaser and distracts DM which lets the Enterprise go.
- Enterprise fires phaser to get DM to chase it instead of the Constellation
- Enterprise is in danger of running out of fuel in 7 hours at rate of expenditure in order to stay ahead of the gaining DM.
The Enterprise has to labor to outrun the machine.
At first the DM is gaining on the Enterprise (just before #4).
SULU: It's closing on us, Mister Spock.
SPOCK: Closing, Captain.
The Enterprise is hit with DM ray.
Following this, we return to the Constellation for a scene to listen to Kirk grumble about being stuck, blind, and deaf (and paralyzed!).
Next, we cut back to the Enterprise and find out that they have only just then managed to outrun the thing. Even after the first attack we learn that the Enterprise's engines are still "operative" (which appears to indicate no significant damage).
Two Major Points to Consider Here
1. The implication of all this is that the DM is capable of traveling at high warp and that the Enterprise (when undamaged) is only just a bit faster.
We aren't talking about a drag race between Ferrari and Chevy Cobalt, but something more like a showdown between a Ferrari and a Lamborghini. The Enterprise would not have realistically had enough time to circle back to the Constellation, warn Starfleet*, and then race ahead to Rigel to offer a defense (as some here have argued).
2. After the Enterprise is damaged at #7, she has no realistic chance of outrunning the DM; consequently Spock's logic at this point does not hold.
DECKER: Mister Spock, status report.
SPOCK: Warp drive and deflectors will be out for a solar day. Repairs proceeding on transporter and communications.
SULU:
It's closing with us again, sir.
DECKER: Maintain speed and distance.
SULU: It's sucking in space rubble from those destroyed planets. Refueling itself.
SPOCK: We can maintain this speed for only seven hours before we exhaust our fuel, but it can refuel itself indefinitely.
DECKER: Then we'll have to fight it now before it gets any stronger.
SPOCK: Illogical. We cannot destroy it. Therefore, we cannot save Rigel.
We must transport the Captain and the others from the Constellation and escape this thing's subspace interference in order to warn Starfleet Command.
As I pointed out up-thread, beaming aboard the Captain only dooms him to the same fate, and they have no chance of outrunning the thing's subspace interference, since they are being pursued by the DM.
You can't get out of jamming range, if the jammer is pursuing you faster than you can run.
*the subspace interference spans across many star systems:
DECKER [OC]: Captain's log, stardate 4202.1. Exceptionally heavy subspace interference still prevents our contacting Starfleet to inform them of the destroyed solar systems we have encountered. We are now entering system L-374. Science Officer Masada reports the fourth planet seems to be breaking up. We are going to investigate.
We cannot know precisely what the distance between these star systems is, but a conservative estimate would be about 10 light years (a little more than twice the distance from Earth to Alpha Centauri).
Would you give a Lamborghini a ten mile head start in a race to the next town?