Amino-adenosine and a complex aromatic ester form a product which autocatalyzes in chloroform. We can say that some do. Some receive energy and nutrients passively. Others actively obtain their sustenance through simple chemistry-mediated searches. All multi-celled plants satisfy the continuity criterion.
Computers are an odd case.
It may be interesting to see how they compare with the other classes of entities when judged by the same criteria. Computers passively retain their structure over time because they are composed of inert materials. Those computers equipped with robotic appendages can replace parts which have failed, and thereby actively maintain themselves. So by passive or active means all computers satisfy the continuity criterion. All invertebrates satisfy the continuity criterion.