I haven't seen it written where you have to maintain the minimum preheat temp until the weld is completed (except when PWHT is required). You do have to make sure you have the minimum preheat/interpass while you are welding, but you could "go to lunch" allowing the joint to cool and then re-heat it before you weld again. Of course, as you indicate, it isn't necessarily a good idea to do that, but you could do that.
An exception is that Section 12 has a provision in 12.15.2.1 that says not to let the weld cool below minimum preheat/interpass prior to PWHT. I take that to mean, once you start welding, you have to follow through without any cooling below minimum.
CHGuilford

The answer by CHGuilford I think answers the "code question". Usually such questions are asked after something "went wrong" according to an inspector, or there are practical difficulties in complying with the requirement. I thought that maybe if we considdered the "fundamentals", we could come to a decision based on "good engineering judgement" that could help you to decide on how to resolve any possible difficulties.

Pre-heat is generally applied for two reasons:

1) To reduce the cooling rates.
2) To keep the temperature of the weldment above some minimum temperature, below which "something bad happens."

Reason 1 is typically used in instances where, if the differential temperature between the parent metal and weld metal is too high, excessively brittle microstructures could form, or excessive distortion could result, or excessive residual stresses could appear in the weldment. If your pre-heat is for this reason, then there is generally no problem in leaving the job to cool down and pre-heating again later before you start welding again.

Reason 2 is typically used in instances where you know that the microstructure formed WILL be hard and brittle (e.g. Cr-Mo materials) and should the temperature fall below a certain value, (e.g. 250°C) hydrogen cracking will most probably result. This is so because below this temperature the solubility of H2 in steel suddenly decreases, leading to potential cracking problems. (You definately have two of the three pre-conditions for H2 cracking present. (1)A susceptible microstructure (2)Stresses. Should the third one, the presence of H2 also be there, then...)

But what if you, unwittingly, let this weldment cool down? Is it necessarily scrap? I believe not. Firstly, make sure that it gets its PWHT ASAP, because H2 cracking can still develop up to 72 hrs after completion of the weld. (Some reports show that it can be even longer.) Then you need to perform some sort of NDT that will show you if you have "contracted" H2 cracking. This would typically involve a surface technique such as MPI, and a sub-surface technique such as UT.

Just an important point. If you are welding a material that is very hardenable, (e.g. Cr-Mo) then the temperature at which the Martensite transformation is complete can be rather low. Should your interpass temperature be too high, followed by directly inserting into the PWHT cycle, you could have retained austenite in your structure. When you cool the weldment down following PWHT, this will transform to martensite, resulting in an excessively hard weld zone. It is therfore important to ensure that the temperature first comes down to approximately the pre-heat temp before going into the PWHT cycle. It is also good practice to perform hardness tests following PWHT, and if the material is too hard, performing another PWHT cycle.

What if your weldment is of such a construction that it is not feasible to keep at the pre-heat temperature untill you can PWHT? Then you have a complicated procedure as follows:

1)Pre-heat.
2)Weld, controlling interpass temperature.
3)Allow to cool to close to pre-heat temp. (To ensure that martensite transformation is complete.)
4)Take back up to a temperature to "bake out" the hydrogen. (Needs to be calculated, based on the material hardenability, weld constraint, material thickness and anticipated H2 content of the weld metal.)
5)Cool to room temperature.
6)Continue with the rest of your welding operation, following above procedure.
7)After 72 hrs, perform NDT to ensure no problems.
8)Perform PWHT.

As long as all parties agree to the above procedure, there is no reason why it should not be acceptable.

Regards
Niekie