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For Altivar 312/32/61/71 range of drives, Is it possible to continue motor operation at same speed even if 4-20 mA analog signal is lost during drive is running.

Yes, it is possible to maintain the speed of motor even if 4-20 mA analog signal is lost during drive is running and so it prevents motor to stop or trip on a fault such
as LFF2 , LFF3 & LFF4 (4-20 mA loss fault detected on AI2, AI3 and AI4 terminals respectiviely) .

To have this function, set parameter LFL2 [ AI2 4-20 mA loss] to rLS [ Spd maint.] Same function can be made available for AI2 and AI3 by setting LFL3 [ AI3 4-20 mA loss]
and LFL4 [ AI4 4-20 mA loss] parameters respectively. These parameters are at FLt [ Fault Management] menu, LFL- [ 4-20 mA loss] sub-menu.

When 4-20 mA signal loss is detected on analog input terminals, drive will continue at the speed which is at the instance 4-20 mA signal loss is detected and
continued till the 4-20 mA signal is restored back. Once 4-20 mA signal is restored, drive automatically follow the speed in accordance with it.

Note, if drive is powered OFF in condition of 4-20 mA signal is lost then after power cycle, drive frequency reference will remain at 0 hZ.  
To resume the speed, 4-20 mA signal has to be restored first.
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