LDO linear regulator output problem
Problem #1
When the output finally turns off in your test, it follows a decay path that tells of an RC influence.  There is some current being discharged through the high internal resistance (spec'ed at up to 2.6MOhm).  The TLS715B0 datasheet also shows a fairly low threshold for EN, using the bandgap reference; a comparator  may have some bias/leakage that counter-acts the pull-down.
Solution
Add an external pull-down (1.5k, 1/4W would be more than sufficient) if you want to control EN, otherwise just short-circuit EN to your input voltage so the LDO is always enabled.
Problem #2
You have an unstable feedback loop between the LDO's protection circuits and the software-controlled constant-current load.
You are pushing the edge of the regulator's thermal and current limits.  The thermal protection circuit may be participating, but I think it is a minor player from how fast this is oscillating.  The over-current protection recovers more quickly and is likely more sensitive at high temperature.
When you increase the input voltage, you increase the voltage drop across the LDO and thus its absorbed power.  This starts to engage the protection circuit(s), dropping the output voltage.  The constant-current load senses its voltage dropping and tries to maintain a constant current by decreasing its resistance.  In the meantime, the protection circuit is successful and the output is again activated - with a stronger (lower R) load - causing the output current to max out.  Lather, rinse, repeat.  Each cycle happens fast enough that the software controlled load cannot react to stabilize the output current.
Experiment
Repeat your test with an equivalent resistive load; the thermal protection may still kick in (it is consuming (18V-5V)*150mA = 2W), but the output current will not spike over the limit and it should not oscillate so fast.