All secured and tight, it's been cleaned
Doesn't mean that the cable itself is not corroded internally.
There are ppl who advocate hitting a starter motor with a hammer a few times (lightly), but in some cases it might damage it.
What I would do if I would have a car with this kind of issues, I would measure the voltage at the starter pins when someone else is trying to start the car. The problem here is that starter is a high current circuit, so measuring resistance of the cable will not help, it needs to be tested for voltage drop under load.
So, plan of attack (have a voltmeter handy in the car) when it won't start again:
1. light taping with hammer (be gentle) on the starter motor... Try to start ... If the problem is gone, it should start no problem. In this case, consider "a new starter investment".
2. ask someone to put the key into "crank" position and measure the voltage at starter pins. Post here what it reads ... Could be the issue with the cable itself. If it is internally corroded, it will misbehave under load.
3. Could be the issue with grounding on the block (I guess that is where the starter takes it's ground from). Check the block ground under load. (again, don't just blindly measure resistance between block and battery ground. Do a voltage drop test under load.)
Don't start throwing parts at it without diagnostics.