sampleRegions deleting input feature collection properties, how to stop that?

You can define the argument properties to do that. See the explanation GEE provides in the documentation on sampleRegion():

properties (List, default: null): The list of properties to copy from each input feature. Defaults to all non-system properties.

An example would be:

// define sample image and feature collection
var sampleFeatCol = ee.FeatureCollection([
  ee.Feature(point1, {prop1: 1, prop2: 2, 'system:time_start': 10000}),
  ee.Feature(point2, {prop1: 2, prop2: 1, 'system:time_start': 10000})]);
var image = ee.Image(1);

// define the properties to retain
var listProperties = ['prop1','system:time_start'];

sampleFeatCol = image.sampleRegions(sampleFeatCol, listProperties, 100)

print(sampleFeatCol)

link example code