That's a tough situation. Can you create assignments that have levels of accomplishment? If you get this done, you get 100, if you get this you get...?
Make it challenging enough so student must work hard for a passing grade.
Try designing assignments so that they are based on Blooms Taxonomy. Reaching evaluation and clearly communicating that ability should be the highest grade. Students who reach
1. Knowledge: arrange, define, duplicate, label, list, memorize, name, order, recognize, relate, recall, repeat, reproduce state. (50%)
2. Comprehension: classify, describe, discuss, explain, express, identify, indicate, locate, recognize, report, restate, review, select, translate, (60%)
3. Application: apply, choose, demonstrate, dramatize, employ, illustrate, interpret, operate, practice, schedule, sketch, solve, use, write. (70%)
4. Analysis: analyze, appraise, calculate, categorize, compare, contrast, criticize, differentiate, discriminate, distinguish, examine, experiment, question, test. (80%)
5. Synthesis: arrange, assemble, collect, compose, construct, create, design, develop, formulate, manage, organize, plan, prepare, propose, set up, write. (90%)
6. Evaluation: appraise, argue, assess, attach, choose compare, defend estimate, judge, predict, rate, core, select, support, value, evaluate. (100%)
If you do this for all those short assignments, more students will work for longer periods, but all will be successful. It may take a couple of years, but eventually, you won't have this problem and all students will successfully pass your class.