Continuous monitoring is extremely challenging still because ECG data needs to be sampled at a relatively high frequency (~200 Hz) to accurately identify the QRS complex in the waveform. That uses a lot of power, and the batteries we have still aren't good enough to support those types of demands. 200 * 60 * 60 = 720,000 samples per hour to collect and process.
It's possible that algorithmic approaches may be able to reduce the sampling frequency required. Power-constraints were the main issue when I studied this topic 10 years ago during my master's degree. I had looked into non-frequency domain techniques (such as empirical mode analysis/Hilbert-Huang transform) as a possible way to reduce sampling frequency and thus power consumption.
https://github.com/AshwinSundar/Empirical-Mode-Decomposition...