Comment on any of these if more detail is anted:
Easy enough electronically, and I'd recommend an electronic solution - but a relay with at least either 1 x changeover contact or 1x make and 1 x break contact will do this. Relay is rated at lowest value current that you want. Place a wirewound pot of suitable rating in parallel to desensitise it by shunting some of the current.
The relay's break contact disconnects the supply. The relay's make contact self latches itself.
Electronic: A foldback current limiter will do what you want. When current exceeds a trip point the circuit adds resistance until some lesser value is reached. This can be latching.
Example from here - at bottom of page. Circuit explanation given on that page.

Measured and calculated performance (from their site).

A circuit that powers itself completely off when a set current is exceeded is also "easy enough".
eg Placing a diode in series with R4 in the above circuit so the diode conducts when LM317 output is low, and lowering the value of R4 to around a few hundred ohms would probably make the circuit fully latching. May not then start well - may need a little thought to tidy the result.
Here is an electronic fuse circuit using a relay as the output switch and a flip flop to latch the tripped state. The relay could be replaced by a MOSFET and the latch could be replaced by hysteresis feedback.
I drew up a circuit before I saw the above which does much the same but removes the latch and uses a MOSFET. It uses 1 x opamp section, 1 x MOSFET, 1 a voltage reference (or a zener with less precision), 5 or 6 resistors, a diode and a pot to set trip level. Turnoff is complete and instant on exceeding Itrip and it latches off. Trip delay can be added with one capacitor and operation can be switched to constant current limit by opening the diode circuit. Can draw (slightly) more tidily and post if needed.
Here is their circuit.

3 transistor foldback current limiter:
Second circuit on page here.
This too can be made to latch off.

A few idea starters here Gargoyle "foldback current limit circuit" image search
Gargoyle "electronic fuse circuit" image search
Just using a constant current source may suffice - so that current can not go above some preset limit.
Best Answer
Trip cycle or trip endurance are the measures that you are looking for. The first is the number of times you can trip and assume that damage to the part has not occurred, the second is the length of time the trip state can be active for before the part is damaged.
Many factors will also determine whether the PTC becomes damaged or not, heat, humidity, age, etc. and it is impossible to determine when the fuse will fail. Normally the point of putting one of these in a system is that the replacement cost of the PTC is less than the replacement cost of the components it is protecting. Think of every trip as one get-out-of-jail-free over traditional fuses.
These are a last line of defence and don't assume that the fuse will always trip to protect your circuit. I hate to think about the number of times a $100 tweeter in my stereo has blown to save the $0.10 protection fuse.